Question

the length of a rectangle is 4 meters less than twice its width. The area of the rectangle is 70. Find the dimensions of the rectangle

Answer 1

Answer:  The width is 7 meters. The length is 10 meters.

Step-by-step explanation:   Area = Length × width

Length is 2w - 4  

Substitute that value for length, then solve for w.

70 = w(2w - 4)

70 = 2w² - 4w  reorganize to quadratic equation form

2w² - 4w -70 = 0   These are All even numbers; factor out 2 (divide all by 2)

w² - 2w - 35 = 0  factor this

(w - 7)(w + 5)    set each factor = 0 and calculate the value of w.

w+5=0  w= -5  (disregard this one because dimensions of real rectangles can't be negative)

w - 7 = 0  w = 7   The width is 7

Substitute into the original expressions to get the value of Length.

2(7) -4 = L    14 - 4 = L  The Length is 10.

Check by substituting into the original equation:

w × 2w -4 = 70

7 × 2(7) -4 = 70

7 × 10 = 70    TRUE!

w