Question

Find the perimeter of the rectangle whose length is 24 m & diagonal is 25 m.​

Answer 1

Given :

⬤ Length of Rectangle is 24 m .

⬤ Diagonal of Rectangle is 25 m .

To Find :

⬤ Perimeter of Rectangle .

Solution :

First , We have to Calculate the Breadth of the Rectangle . Hence ,

• Let Breadth of Rectangle be x .

By Pythagoras theorem :-

In ∆BDC ,

(BC)² = (CD)² + (BD)²

(25)² = (24)² + (x)²

(25×25) = (24×24) + (x)²

625 = 576 + (x)²

625 - 576 = (x)²

49 = (x)²

√49 = x

7 = x

Therefore , The Breadth (x) of the Rectangle is 7 m .

Formula Used :

$\bf[\:{Perimeter \: of \: Rectangle = 2(l+b)}\:]$

Solution :

• Length = 24 m.
• Breadth = 7 m .

According to the Formula :-

2 (l + b)

2 (24 + 7)

2 (31)

62

Therefore , The Perimeter of Rectangle is 62 m .

Answer 2

Answer:

It is given that,

Length = 24 cm.

Diagonal = 25 cm.

Consider the breadth of a rectangle = b m.

Using Pythagoras theorem in triangle ABC,

AC^2 =AB^2 +BC^2

Substituting the values,

252=242+b^2

625=576+b^2

By further calculation,

b^2=625–576=49

b= √49 =7 cm.

Here the perimeter of rectangle = 2(l+b)

Substituting the values,

=2(24+7)

So we get,

=2(31)

=62 cm.

Hope this is helpful for you.