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.