Question

A rectangular mural has dimensions of (x + 10) and (x + 3) feet. If the area of the mural is 60

square feet, what are its length and width?

Answer 1

Dimensions are 12 , 5

Explanation:

Area of rectangular mural = length * width

length * width = 60 square feet

(x + 10)(x + 3) = 60

Use FOIL method

x*x + x*3 + 10*x + 10*3 = 60

x² + 3x + 10x + 30 = 60 {Combine like terms}

x² + 13x + 30 - 60 = 0

x² + 13x - 30 = 0

Sum = 13

Product = -30

Factors = 15 , -2 (15+ (-2) = 13 ; 15*(-2) = -30)

x² + 15x - 2x - 30 =0 {Rewrite middle terms}

x(x + 15) - 2(x + 15) = 0

(x + 15)(x - 2) =0

x - 2 = 0 {Ignore (x +15) as dimensions wont have a negative value}

x = 2

x + 10 = 2 + 10 = 12

x + 3 = 2 + 3 = 5

Dimensions are 12 , 5