Question

Tina is making rectangular signs. Each poster has an area of 1800 square inches and the length is 30 inches more than the width. Find the length and width of her sign. If x represents the width of each sign, select all of the equations that could be used to solve this problem. 2(x)+2(x+30)=1800 (x+30)(x)=1800 x(30x)=1800 x(x+30)=1800 Part 2 Find the dimensions of each rectangular sign. width = inches length = inches

Answer 1

Let the width be x. Since the length is 30inches longer than the width, the length is 30 + x.
Area = length x width = (30 + x)(x)
i.e. (30 + x)(x) = 1800 square inches.

$30x + x^{2} =1800 \\ x^{2} +30x-1800=0 \\ x^{2} -30x+60x-1800=0 \\ ( x^{2} -30x)+(60x-1800)=0 \\ x(x-30)+60(x-30)=0 \\ (x+60)(x-30)=0$
x + 60 = 0 or x - 30 = 0
x = -60 or x = 30
but the width cannot be a negative number, hence x = 30inches
i.e. width = 30 inches
length = 30 + 30 = 60 inches.