Question

The length and breadth of a rectangle are in the ratio of 4 : 3 . If the diagonal measures 25 cm the perimeter of the rectangle is

Answer 1

the perimeter is 14cm

Step-by-step explanation:

say, the sides are 4x cm and 3x cm respectively.

then,

(4x)² +(3x)²= 25

or,16x² + 9x²= 25

or, x=1

then, the sides are 4cm and 3cm

• perimeter={2(4+3)}cm=14cm

Answer 2

Given :

• The ratio of length and breadth = 4:3.
• Length of diagonal = 25 cm

To find :

• the perimeter of the rectangle.

Solution :

⇒ Let's find the length and breadth of the rectangle.

• Let us take the length to be 4x and the breadth to be 3x.

$\sf \longrightarrow c^2 = a^2 + b^2$

$\sf \longrightarrow 25^2 = 4x^2 + 3x^2$

$\sf \longrightarrow 625 = 16x + 9x$

$\sf \longrightarrow 625 = 25x^2$

$\sf \longrightarrow x^2 = \dfrac{625}{25}$

$\sf \longrightarrow x^2 = 25$

$\sf \longrightarrow x = \sqrt{25}$

$\sf \longrightarrow x = 5$

$\sf \therefore x = 5$

$\sf \rightarrow Length = 4x$

$\sf = 4 \times 5$

$\sf = 20 \: cm$

$\sf \rightarrow Breadth = 3x$

$\sf = 3 \times 5$

$\sf = 15 \: cm$

Perimeter of Rectangle = 2 (l + b)

= 2 (20 + 15)

= 2 (35)

= 2 × (35)

= 70 cm

• Therefore, the perimeter of the rectangle is 70 cm.