Question : The difference between the length and breadth of a rectangle is 40 metres. If its perimeter is 96 metres, then what will be the area of the rectangle?
Option 1: 254 m2
Option 2: 110 m2
Option 3: 176 m2
Option 4: 152 m2
Correct Answer: 176 m 2
Solution :
Let $l$ be the length and $b$ be the breadth.
$l-b = 40$
⇒ $l = 40+b$ ---------(i)
Perimeter = 96 m
$2(l+b) = 96$
⇒ $2(40+b+b) = 96$
⇒ $40+2b = 48$
⇒ $2b = 48-40 = 8$
⇒ $b = 4$
⇒ $l = 40+4 = 44$
Area = $lb = 4×44 = 176$
Hence, the correct answer is 176 m
2
.
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