sides of rectangle (x+7) cm, (x+3) cm, area of the rectangle is 45cm^., Find the lenght of the sides

Question

The sides of a rectangle are, (x+7)cm, and (x+3) cm, and the area is 45cm^. Find the length of sides. Factoring also.

Answer 1

Area of a rectangle is length times width

(x+7)(x+3) = 45

FOIL on the left

x^2 + 3x + 7x + 21 = 45

combine like terms

x^2 + 10x + 21 = 45

subtract 45 from both sides

x^2 + 10x - 24 = 0

factor, what multiplies to make 24 and subtracts to make 10?

that would be 12 and 2

so (x+12)(x-2) = 0

set each equal to 0

x+12 = 0 so x = -12

x-2 = 0 so x= 2

the answer cannot be -12 because that creates negative lengths

therefore x=2 is the correct answer

so 2+7 and 2+3 makes it 9 by 5