Question

The rectangle below has an area of x^2-7x+10square meters and a width of x - 5 meters. What expression represents the length of the rectangle below? length=_____ meters.

Answer 1

L = (x - 2) meters

Explanation:

The area of the rectangle = (x² - 7x + 10) m²

The width = (x - 5) m

length = ?

Area of a rectangle = length × width

x² - 7x + 10 = L(x -5)

note L = length

divide both sides by (x-5)

(x² - 7x + 10)/(x - 5) = L

L = x² - 7x + 10 / (x -5)

Factorize x² - 7x + 10

find the numbers you can multiply to give you 10 and also add to give you -7

The numbers are -2 and -5. Therefore,

x² - 2x - 5x + 10 = 0

x(x - 2) - 5(x - 2) = 0

(x-5)(x-2) = 0

Let us go back to our division

L = x² - 7x + 10 / (x -5)

x² - 7x + 10 = (x-5)(x-2)

L = (x-5)(x-2) / (x -5)

L = (x - 2) meters