Question

The area of a rectangular room is 10. Its perimeter is 14. What are the sides? ( A ) 5,5 ( B ) 7,2 ( C ) 5,2 ( D ) 8,6

Answer 1

let the length be l and breadth be b .

therefore area = l× b= 10

l= 10/b

again

perimeter = 2(l+b) = 14

$l + b = 7 \\ \frac{10}{b} + b = 7 \\ \frac{10 + {b}^{2} }{b} = 7 \\ {b}^{2} + 10 = 7b \\ {b}^{2} - 5b - 2b+ 10 = 0 \\ b(b - 5) - 2(b - 5) = 0 \\ (b - 2)(b - 5) = 0 \\ either \: \: \: b = 2 \: \: \: \: or \: b = 5$

therefore length = 10 / 2 = 5.

hence the side are 5,2.