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

Answer:

1st garden area = 126 sq mts

2nd garden area = 119 sq mts

second garden is smaller

Step-by-step explanation:

1st garden

width = x, length = x + 5

area = x × (x + 5)

2nd garden

width = x - 2, length = x + 8

area = (x - 2)(x + 8)

${x}^{2} + 6x - 16 = 119 \\ {x}^{2} + 6x - 135 = 0 \\ {x}^{2} + 15x - 9x - 135 = 0 \\ x(x + 15) - 9(x + 15) = 0 \\ (x + 15)(x - 9) = 0 \\ x + 15 = 0 \: \: \: \: x - 9 = 0 \\ x = - 15 \: \: \: \: \: \: x = 9$

as length cannot be negative we take x = 9

area of 1st garden x ×(x+5)= 9 × (9 + 5)

9 × 14 = 126 sq mts