Answer: 4x2 + 32x − 80 = 0
Step-by-step 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:
width = 12 (approx.)
Step-by-step 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
∴[tex]x = -\frac{7}{2}+\frac{1}{2}\sqrt{161}[/tex]
= 2.84
or [tex]x = -\frac{7}{2}-\frac{1}{2}\sqrt{161}[/tex]
= - 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.)
