Question

You plan to build a house that is 1 ½ times as long as it is wide. You want the land around the house to be 20 feet wider than the width of the house, and twice as long as the length of the house, as shown at the right.

Write an expression for the area of the land surrounding the house.

Answer 1

let the width of house be x

hence length of house is 1.5x

area of house = length × width = 1.5x × x

$= 1.5 {x}^{2}$

for total area along with land,

width = x + 20

length = 3x

total area along with land = length × breadth

$= 3x \times (x + 20)$

area of land =

total area along with land - area of house

$= 1.5 {x}^{2} \times 3x(x + 20) \\ = 4.5 {x}^{3} \times (x + 20)$