Prove that diagonals of rectangle are of equal length.

Land is acquired for road widening from a square ground, as shown in the figure. The width of the acquired land is $2 \mathrm{m}$. Area of the remaining ground is $440 {\mathrm{m}}^2$. What is the shape of the remaining ground?

X, Y and Z are the midpoints of the sides of ∆PQR. If the perimeter of ∆XYZ is 32 units, find the perimeter of ∆PQR.

 (A) 128 units 

(B) 64 units 

(C) 96 units 

(D) 160 units 

The perimeter of a rectangle is 42 cm. If its diagonal is 15 cm long, find the breadth of the rectangle. 

(A) 8 cm. 

(B) 10 cm. 

(C) 9 cm. 

(D) 7 cm. 

A and B are the endpoints of line segment AB. If $\mathrm{CA}\perp \mathrm{AB}$ and $\mathrm{DB}\perp \mathrm{AB}$ and $\mathrm{CA}=\mathrm{DB}$. What figure will you get if you join CD?

Jose and Rahim have $16$ matchsticks each. All of the same length. Which is wider?

In a $\Delta ABC$ $\angle A: \angle B : \angle C =2 : 3 : 4$. $A$ line $CD$ drawn to $AB$. then the $\angle ACD$ is:

In the above rectangle, $ABCD$ find out '$BO$'?