The length of one diagonal of a rectangle is 5 cm. If the ratio of the length and breadth of the rectangle is 4 :3, then the perimeter of the rectangle is____

Q. The length of one diagonal of a rectangle is 5 cm. If the ratio of the length and breadth of the rectangle is 4 :3, then the perimeter of the rectangle is____           

(ADRE 2024)

(A) 25 cm

(B) 14 cm

(C) 12 cm

(D) 16 cm

Answer:- (B) 14 cm

Solution :- Let the length of the rectangle be 4x and the breadth be 3x.

Given, the length of one diagonal = 5 cm

Using Pythagoras theorem, we get:
⇒ (4x)²  + (3x)² = 5²
⇒ 16x²+ 9x² = 25
⇒ 25x² = 25
⇒ x² = 1
⇒ x = 1

So, length = 4x = 4 cm
Breadth = 3x = 3 cm

Perimeter of the rectangle = 2(length + breadth) = 2(4 + 3) = 2× 7 = 14 cm

Therefore, the perimeter of the rectangle is 14 cm.

So, the answer is (B) 14 cm.