Question

The area of a rectangular placemat is 168 square inches. Its length is two inches longer than the width. Find the length and width of the placemat.

Answer 1

Answer:

length = 14 inches

breadth = 12 inches

Step-by-step explanation:

area of rectangle = l × b = 168

let the breadth be x

the length will be x + 2

$x \times (x + 2) = 168 \\ {x}^{2} + 2x = 168 \\ {x}^{2} + 2x - 168 = 0 \\ {x}^{2} + 14x - 12x - 168 = 0 \\ x(x + 14) - 12(x + 14) = 0 \\ (x + 14)(x - 12) = 0 \\ x + 14 = 0 \: \: \: \: \: \: x - 12 = 0 \\ x = - 14 \: \: \: \: \: \: \: \: \: x = 12 \\ we \: take \: the \: positive \: value \: of \: x \\ breadth \: = x = 12 \\ length \: = x + 2 = 12 + 2 = 14$