The sides of a rectangle are in the ratio $5 : 3$ and its perimeter is $112 ext{ cm}$. The area of this recta

Question

The sides of a rectangle are in the ratio $5 : 3$ and its perimeter is $112	ext{ cm}$. The area of this rectangle is:

Examoogle · Accepted Answer

The correct answer is Option A: 735 $	ext{cm}^2$. Sum of ratio parts = $5+3=8$. Half-perimeter (semi-perimeter) = $112 / 2 = 56$. Side $l = (5/8) 	imes 56 = 35$, Side $b = (3/8) 	imes 56 = 21$. Area = $35 	imes 21 = 735$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Sum of ratio parts = $5+3=8$. Half-perimeter (semi-perimeter) = $112 / 2 = 56$. Side $l = (5/8) 	imes 56 = 35$, Side $b = (3/8) 	imes 56 = 21$. Area = $35 	imes 21 = 735$.

Formula Used: $$P = 2(l + b), 	ext{Area} = l 	imes b$$

Given: Ratio of sides = 5 : 3, Perimeter = 112 cm

Steps: Define sides in terms of x: Let the length be $l = 5x$ and breadth be $b = 3x$.. Use perimeter formula: Perimeter $P = 2(l + b) = 112$. Substituting $l$ and $b$: $2(5x + 3x) = 112$.. Calculate x and dimensions: Solving for $x$: $x = 112 / 16 = 7$. Thus, $l = 5(7) = 35$ cm and $b = 3(7) = 21$ cm.. Calculate Area: Area $A = l 	imes b = 35 	imes 21 = 735$ square cm.

Answer: A is correct because the length is 35 cm and breadth is 21 cm, resulting in an area of 735 cm².

Exam Tip: This ratio method is fundamental for all geometry problems involving dimensions like triangles and circles where constraints are given in terms of specific ratios.

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