Answer:
width = 9/2 m
length = 14 m
Step-by-step explanation:
Let width = x
If the length of a rectangle is 5 m more than twice the width:
⇒ length = 2x + 5
Use the given information to create a quadratic equation:
Area of a rectangle = width × length
⇒ 63 = x(2x + 5)
⇒ 63 = 2x² + 5x
⇒ 2x² + 5x - 63 = 0
Find the value of x by factorizing the quadratic:
⇒ 2x² + 5x - 63 = 0
⇒ 2x² + 5x - 63 = 0
⇒ 2x² + 14x - 9x - 63 = 0
⇒ 2x(x + 7) - 9(x + 7) = 0
⇒ (2x - 9)(x + 7) = 0
Therefore:
⇒ (2x - 9) = 0 ⇒ x = 9/2
⇒ (x + 7) = 0 ⇒ x = -7
Width cannot be negative, therefore, x = 9/2 only
⇒ width = 9/2 m
⇒ length = 2(9/2) + 5 = 14 m
