Question

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

a) 56 cm
b) 60 cm
c) 70 cm
d) 80 cm

I need step by step explanation
No Direct Answer

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Answer 1

Step-by-step explanation:

let x be the common multiple

length =4x

breadth =3x

according to pythagoras theorem

(4x)²+(3×)²=(25)²

16ײ+9ײ=625

25ײ=625

x²=625/25

X=5

so,

length =4×=20cm

breadth =3×=15cm

perimeter = 2(lxb)

=2(20+15)

=70cm

so, perimeter of rectangle is 70cm

hopefully this will help you

Answer 2

Given,

$\red\diamond$length and breadth of a rectangle are in the ratio 4:3

$\red\diamond$diagonal= 25 cm

Let,

$\red\diamond$the length = 4x and

$\red\diamond$the breadth = 3x

According to the Pythagoras theorem,

$\longmapsto\tt{(4x)^{2}+(3x)^{2}=252}$

$\longmapsto\tt{16x^{2}+9x^{2}=625}$

$\longmapsto\tt{25x^{2}=625}$

$\longmapsto\tt{x^{2}=\cancel\frac{625}{25}}$

$\longmapsto\tt{x^{2} =25}$

$\longmapsto\tt{x=\sqrt{25}}$

$\longmapsto\tt\boxed{x=5}$

the measure of,

Length = 4x = 4 × 5 = 20 cm

Breadth = 3x = 3 × 5 = 15 cm

$\boxed{\therefore Perimeter= 2(l +b) = 2(20+15) = 2(35) = 70 cm}$

hence, (c) 70cm is the correct option.

hope it helps:)