Question

6. The area of a rectangular sheet of paper is 300 cm squared. The length is 5 cm more than the width

a) If the width of the rectangle is x cm, state an expression for the length of the rectangle.
b) Write and algebraically solve a quadratic equation to determine the length and
width of the rectangle.

Answer 1

a) length = x + 5

b)
`x^(2)` + 5x - 300 = 0

Explanation:

x = width

x + 5 = length

(x)(x + 5) = 300

`x^(2)` + 5x = 300

`x^(2)` + 5x - 300 = 0

(x+20)(x-15)

x = -20 or x = 15 ( disregard the -20. measurements can't be negative)

width = 15

length = x+ 5 = 15+5 = 20

Answer 2

Explanation:

width = x

length= x + 5

a) x + 5

b) x * (x+5) = 300

x^2 + 5x = 300

x^2 + 5x - 300 = 0

Δ = 25 + 1200 = 1225

width = (-5 + 35)/2 = 15 cm

lenght = 15 + 5 = 20 cm