Answer:
Length = 16 feet, Width = 20 feet
Explanation:
Area of a rectangle is L x W where
L = length
W = width
We are given
L = (x + 10) feet
W= (x + 14) feet
area = 320 square feet
Using the equation for area as L x W
(x + 10) (x + 14) = 320
(x + 10) (x + 14) can be evaluated using the FOIL method
x² + 14x + 10x + 10 x 14
= x² + 24x +140
→ x² + 24x + 140 = 320
→ x² + 24x + 140 - 320 = 0
→ x² + 24x - 180 = 0
This is a quadratic equation which can be solved using either the quadratic formula or factoring
Using factoring:
x² + 24x - 180 :
→ x² - 6x + 30x -180
→ x(x - 6) + 30(x - 6)
Factoring out common expression (x-6) we get
x² + 24x - 180 : (x - 6) (x + 30)
And knowing the right side is 0 we get
(x - 6) ( x + 30) = 0
This means either x - 6 = 0 ==> x = 6
or
x + 30 = 0 giving x = -30
ignoring the negative solution we get
x = 6
Plugging this back into the expressions for L and W
L = x + 10 = 6 + 10 = 16
W = x + 14 = 6 + 14 = 20
Therefore length = 16 feet, width = 20 feet