# Recent questions tagged geometry

1

In a triangle $\text{ABC}, \angle \text{BCA} = 50^{\circ}. \text{D}$ and $\text{E}$ are points on $\text{AB}$ and $\text{AC},$ respectively, such that $\text{AD = DE}.$ I...

2

Let $\text{ABCD}$ be a parallelogram. The lengths of the side $\text{AD}$ and the diagonal $\text{AC}$ are $10 \; \text{cm}$ and $20 \; \text{cm},$ respectively. If the a...

3

The cost of fencing a rectangular plot is $ \text{₹} \; 200 \; \text{per ft}$ along one side, and $ \text{₹} \; 100 \; \text{per ft}$ along the three other sides. If ...

4

A park is shaped like a rhombus and has area $96 \; \text{sq m}.$ If $40 \; \text{m}$ of fencing is needed to enclose the park, the cost, in $\text{INR},$ of laying elect...

5

If a rhombus has area $12 \; \text{sq cm}$ and side length $5 \; \text{cm},$ then the length, $\text{in cm},$ of its longer diagonal is$\sqrt{13} + \sqrt{12}$$\sqrt{37} +...

6

The sides $\text{AB}$ and $\text{CD}$ of a trapezium $\text{ABCD}$ are parallel, with $\text{AB}$ being the smaller side. $\text{P}$ is the midpoint of $\text{CD}$ and $\...

7

Let $\text{D}$ and $\text{E}$ be points on sides $\text{AB}$ and $\text{AC},$ respectively, of a triangle $\text{ABC},$ such that $\text{AD}$ : $\text{BD} = 2 : 1$ and $...

8

If the area of a regular hexagon is equal to the area of an equilateral triangle of side $12 \; \text{cm},$ then the length, in cm, of each side of the hexagon is $6 \sqr...

9

Suppose the length of each side of a regular hexagon $\text{ABCDEF}$ is $2 \; \text{cm}.$ It $\text{T}$ is the mid point of $\text{CD},$ then the length of $\text{AT, in ...

10

A circle of diameter $8 \; \text{inches}$ is inscribed in a triangle $\text{ABC}$ where $\angle \text{ABC} = 90^{\circ}.$ If $\text{BC} = 10 \; \text{inches}$ then the ar...

11

The vertices of a triangle are $(0,0), (4,0)$ and $(3,9).$ The area of the circle passing through these three points is $\frac{14 \pi}{3}$$\frac{12 \pi}{5}$$\frac{123 \pi...

12

The points $(2,1)$ and $( – 3, – 4)$ are opposite vertices of a parallelogram. If the other two vertices lie on the line $x + 9y + c = 0,$ then $\text{c}$ is $12$$14$...

13

In a trapezium $\text{ABCD},\; \text{AB}$ is parallel to $\text{DC}, \; \text{BC}$ is perpendicular to $\text{DC}$ and $\angle \text{BAD} = 45^{\circ}.$ If $\text{DC} = 5...

14

The sum of the perimeters of an equilateral triangle and a rectangle is $90 \; \text{c...

15

Let $\text{C}$ be a circle of radius $5 \; \text{meters}$ having center at $\text{O}.$ Let $\text{PQ}$ be a chord of $\text{C}$ that passes through points $\text{A}$ and ...

16

Let $\text{C}1$ and $\text{C}2$ be concentric circles such that the diameter of $\text{C}1$ is $2 \; \text{cm}$ longer than that of $\text{C}2.$ If a chord of $\text{C}1$...

17

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s.$ Then the area o...

18

On a rectangular metal sheet of area $135$ sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thir...

19

A circle is inscribed in a rhombus with diagonals $12$ cm and $16$ cm. The ratio of the area of circle to the area of rhombus is $\frac{5\pi }{18}$ $\frac{6\pi }{25}$ $\f...

20

A circular garden twenty feet in diameter is surrounded by a path three feet wide. What is the area of the path?$51 \pi$ square feet$60 \pi$ square feet$69 \pi$ square fe...

21

What is the area of a semicircle with a diameter of $16$ inches?$32 \pi$ square inches$64 \pi$ square inches$128 \pi$ square inches$256 \pi$ square inches

22

Which of the following figures has the largest perimeter $(1 \text{ foot} = 12 \text{ inches})$a square with a diagonal of $5$ feeta rectangle with sides of $3$ feet and ...

23

The perimeter of a parallelogram is $50$ cm. The length of the parallelogram is $5$ cm more than the width. Find the length of the parallelogram.$15$ cm$11$ cm$5$ cm$10$ ...

24

A conical tent is to accommodate $10$ persons. Each person must have $6\;m^{2}$ space to sit and $30\;m^{3}$ of air to breath. What will be height of cone ?$37.5\;m$$150\...

25

In a swimming-pool $90$ m by $40$ m, $150$ men take a dip. If the average displacement of water by a man is $8$ cubic metres, what will be rise in water level ?$30$ cm$33...

26

If $A$ be the area of a right angled triangle and $b$ be one of the sides containing the right angle, then the length of altitude on the hypotenuse is :$\frac{2Ab}{\sqrt{...

27

In an acute angled triangle $ABC$, if $\tan \left(A+B-C \right)=1$ and $\sec \left(B+C-A \right)=2$, Find angle $A$.$60^\circ$$45^\circ$$30^\circ$$90^\circ$

28

What will be area of the rhombus with equations of sides $ax \pm$ $by \pm c$ = $1$ ?$\frac{3c^{2}}{ab}$sq. units$\frac{4c^{2}}{ab}$sq. units$\frac{2c^{2}}{ab}$sq. units$\...

29

If $\left (-4, 0 \right), \left(1, -1 \right)$ are two vertices of a triangle whose area is $4$ Sq units then its third vertex lies on :$y=x$$5x+y+12=0$$x+5y-4=0$$x-5y+4=...

30

In a triangle $XYZ$, $P$ and $Q$ are points on ${XY,XZ}$ respectively such that $XP=2PY$, $XQ=2QZ$, then the ratio, of area of $\triangle XPQ$ and area of $\triangle XYZ$...

31

A conical tent is to accommodate $10$ persons. Each person must have $6m^{2}$ space to sit and $30m^{3}$ of air to breath. What will be height of cone?$37.5$ m$150$ m$75$...

32

In a bangle shop. If the shopkeeper displays the bangles in the form of a square then he is left with $38$ bangles. If he wanted to increase the size of square by one ban...

33

$A,B,C$ are three towns forming a triangle. A man has to walk from one town to next town, then ride to the next town then again drive towards his starting point. He can ...

34

A cylindrical box of radius $5$ cm contains $10$ solid spherical balls each of radius $5$ cm. If the topmost ball touches the upper cover of the box, then the volume of t...

35

If $(-4,0),(1,-1)$ are two vertices of a triangle whose area is $4$ Sq units then its third vertex lies on:$y=x$$5x+y+12=0$$x+5y-4=0$$x-5y+4=0$

36

For a sphere of radius $10$ cm, the numerical value of the surface area is how many percent of the numerical value of its volume?$26.5\%$$24\%$$30\%$$45\%$

37

Line $AB$ is $24$ metres in length and is tangent to the inner one of the two concentric circles at point $C.$ Points $A$ and $B$ lie on the circumference of the outer ci...

38

A rectangular field is to be fenced on three sides leaving a side of $20$ feet uncovered. If the area of the field is $680$ sq feet, how many feet of fencing will be requ...

39

If $10$, $12$ and '$x$' are sides of an acute angled triangle, how many integer values of '$x$' are possible?$7$$12$$9$$13$

40

The length of a rope, to which a cow is tied, is increased from $19$ m to $30$ m. How much additional ground will it be able to graze ? Assume that the cow is able to mov...