Question

The length of a rectangle is 24 m and its diagonal is 30 m find the breadth and area of the rectangle.

Answer 1

Given

Length of Rectangle is 24m

Diagonal of Rectangle is 30m

To Find

Area of Rectangle

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Since , the breadth is not given and length and diagonal is given.

see in the above figure ,

In∆BDC ,BD= 30cm & CD= 24cm

We have to find BC which is the breadth of the Rectangle

By using Pythagoras theorem in ∆BDC

H²=p²+b²

H is the hypotenuse, p is the perpendicular & b is the base.

In ∆ BDC

BD is the hypotenuse , BC is the perpendicular & CD is the base

➙BD²=BC²+CD²

➙(30)²=BC²+(24)²

➙900= BC²+576

➙BC²= 900-576

➙BC²=324

➙BC=√324=18

Hence, breadth of the Rectangle is 18cm

Check:

Sum of the square of Diagonals of Rectangle is equal to the sum of the square of its length and breadth.

Since , Diagonals of Rectangle are equal.

So, (30)²= (18)²+(24)²

➙900=324+576=900

Answer 2

So, (30)²= (18)²+(24)²

➙900=324+576=900