Question

The length of a rectangle frame is represented by the expression 2x +8, and the width of the rectangle frame is represented by the expression 2x +6 what is the width of the rectangle frame that has a total area of 160 Square inches

Answer 1

Answer: 4x2 + 32x − 80 = 0

Explanation:

Area of a rectangle is given by

A = l*w

The length is (2x+10) and the width is (2x+6)

A = (2x+10)(2x+6)

FOIL

first 2x*2x = 4x^2

outer 2x*6 =12x

inner 2x*10 =20x

last 10*6=60

Add this together

4x^2 +12x+20x +60 = 4x^2 +32x+60

This must equal 140 inches

4x^2 +32x+60 = 140

Subtract 140 from each side

4x^2 +32x+60-140 = 140-140

4x^2 +32x -80=0

Answer 2

width = 12 (approx.)

Explanation:

length = 2x +8

width = 2x + 6

Area of the rectangle frame = 160 square inches

We know

area of the rectangle frame = length x breadth

160 = (2x +8)( 2x + 6 )

(2x +8)( 2x + 6 ) = 160

4x2 + 28x + 48 = 160

4x2 + 28x + 48 − 160 = 0

4x2 + 28x − 112 = 0

Use quadratic formula with a = 4, b = 28, c= -112

x= [ −b±√(b2−4ac)]/2a

Substituting we get

x=[−(28)±√{(28)2−4(4)(−112)}]/2(4)

x= [−28±√(2576)]/8

∴
`x = -(7)/(2)+(1)/(2)√(161)`

= 2.84

or
`x = -(7)/(2)-(1)/(2)√(161)`

= - 9.84

Now measurement cannot be negative, so taking the positve value of x = 2.84 inche we can calculate the width.

We know, width = 2x + 6

=2(2.84) + 6

= 11.68

= 12 (approx.)