Question

the side of the pair of adjecent sodesbof a rectangle are in the ratio3:4.if its diagonal is 20 cm long then find the lengths of tue side hence the perimeter of the rectangle.​

Answer 1

Given that, ratio of sides = 3 : 4

So, let the sides be 3x and 4x respectively.

We know that the sides of a rectangle make an angle of 90°, thus, the diagonal acts as a hypotenuse for the triangle formed by it. Hence, by Pythagoras Theorem,

(3x)² + (4x)² = (20)²

» 9x² + 16x² = 400

» 25x² = 400

» x² = 400/25

» x² = 16

» x = √16

» x = ±4, since, length can't be negative, we will take

x = 4

So, length = 3x = 3(4) = 12 cm

breadth = 4x = 4(4) = 16 cm

So, perimeter = 2(l + b)

= 2(16 + 12)

= 2(28)

= 56 cm

Answer :- Length = 12 cm, breadth = 16 cm and perimeter = 56 cm

Answer 2

Solution:

Given that,
Its Sides Ratio = 4 : 3
Diagonal = 25 cm

Now,
Let length and breadth be 4k and 3k respectively.

By Pythagoras theorem,

⇒ 25²= 4k² + 3k²
⇒ 625 = 16k² + 9k²
⇒ 625 = 25k²
⇒ k² = 625 / 25
⇒ k² = 25
∴ k = 5

Hence,
The length of rectangle = 4k = 20 m
And, breadth of rectangle = 3k = 15 m

Again,
Perimeter of rectangle = 2(l + b)
                                    = 2(20+15)
= 2 × 35
= 70 m

Hence , The Required perimeter of the rectangle is 70 m.