Question

Help me please I need it

Answer 1

Answer:

width = 8 feet and length = 12 feet

Step-by-step explanation:

Let the width be w then the length = 3w - 12 ( 12 less than 3 times the width )

The area (A) of a rectangle is

A = length × width, that is

w(3w - 12) = 96 ← area of floor

3w² - 12w = 96 ( subtract 96 from both sides )

3w² - 12w - 96 = 0 ← in standard form for a quadratic equation

Divide all terms by 3

w² - 4w - 32 = 0

Consider the product of the factors of the constant term ( - 32) which sum to give the coefficient of the w- term (- 4)

The factors are - 8 and + 4, since

- 8 × 4 = - 32 and - 8 + 4 = - 4, hence

(w - 8)(w + 4) = 0

Equate each factor to zero and solve for w

w - 8 = 0 ⇒ w = 8

w + 4 = 0 ⇒ w = - 4

However, w > 0 ⇒ w = 8

Hence width = 8 feet

length = 3w - 12 = (3 × 8) - 12 = 24 - 12 = 12 feet