Question

Harish made a rectangular garden, with its length 5 metres more than its width. The next year, he increased the length by 3 metres and decreased the width by 2 metres. If the area of the second garden was 119 sq m, was the second garden larger or smaller ?

Answer 1

In first case,
Let length of the garden = x m
then width = (x – 5) m
Area = l x b = x(x – 5) sq. m
In second case,
Length = (x + 3)m
and width = x - 5 - 2 = (x - 7)m
According to the condition,
(x + 3)(x - 7) = 119
⇒ x² - 7x + 3x - 21 = 119
⇒ x² - 4x - 21 - 119 = 0
⇒ x² - 4x - 140 = 0
⇒ x² - 14x + 10x - 140 = 0
⇒ x(x - 14) + 10(x - 14) = 0
⇒ (x - 14)(x + 10) = 0
Either x - 14 = 0,
then x = 14
or
x + 10 = 0,
then x = -10,
but it is not possible as it is negative.
∴ Length of first garden = 14m
and width = 14 - 5 = 9m
Area
= l x b
= 14 x 9
= 126m²
Difference of areas of two rectangles
= 126 - 119
= 7sq.m.
∴ Area of second garden is smaller than the area of the first garden by 7 sq.m.