Question

The length of a rectangle is two feet less than 3 times the width. If the area is 65 ft².

Find the dimensions.
Use GUFSA (given, unknown, formula, solution, answer)
comment if you need the steps
this is Grade 8 mathematics

Answer 1

x= width

3x-2 = length

Area= x(3x-2)= 3x²-2x

3x²-2x=65

3x²-2x-65=0

b²-4ac= (-2)²-4(3*-65)= 4+260=784

Δ is strictly positive, the equation 3x²−2x−65=0

admits two solutions.

(-b-√Δ )/2a = (2-28)/6 = -13

(-b-√Δ)/2 =(2+28)/6=5

a length is never negative→x=5

dimensions:

width = 5ft

length = 5*3-2=13 feet

Answer 2

Let l = length of rectangle

w = width of rectangle

l = 3w - 2

w(3w - 2) = 65

3w² - 2w - 65 = 0

(3w + 13)(w - 5) = 0

w = 5 ft, so l = 3(5) - 2 = 15 - 2 = 13 ft