The area of a rectangle is x2 + 7x + 12. Find an expression for the length and width of the rectangle by factoring. If x = 10 cm, find the length and width of the given rectangle.

Answer 1

Length = 13 = (x + 3)

Width = 14 = (x + 4)

x² + 7x + 12 = area of the rectangle

can be factored into

(x + 3)(x + 4)

Let L = one of the factors (x + 3)

Let W = the other factor (x + 4)

If x = 10 then

(10 + 3) = 13 = L

(10 + 4) = 14 = W

Checking this can be checked a couple of ways

Plug x = 10 into the original equation

x² + 7x + 12

10² + 7(10) 12 = 100 + 70 + 12 = 182 = Area

Multiplty the factors

L x W = 13 x 14 = 182 = Area

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