Question

The length of a rectangle is 4cm more than the breadth should the length and breadth be increased by 3cm, the area increases by 81 square cm .what is the length and breadth of the rectangle

Answer 1

let length of a rectangle be x and breadth of a rectangle be y

The length of a rectangle is 4cm more than the breadth
so, x = y + 4........(1)

area of rectangle = (y+4)y = y² + 4y

the length and breadth be increased by 3cm, the area increases by 81 square cm
so, length = x + 3 = y + 4 + 3 = y + 7
breadth = y + 3
area of rectangle = y² + 4y + 81
(y+7)(y+3) = y² + 4y + 81
y² + 3y + 7y + 21 = y² + 4y + 81
y² + 10y + 21 = y² + 4y + 81
y² + 10y + 21 - y² - 4y - 81 = 0
6y - 60 = 0
6y = 60
y = 60/6
y = 10 cm

x = 10+4 = 14 cm

so, length is x = 14cm and breadth is y = 10 cm

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