Question

My new TV has a perimeter of 164 inches. Its width is 8 inches less than twice the height. How many inches wide is the TV?

Answer 1

The perimeter is the sum of the lengths of all sides. A rectangle has two equal lengths and two equal widths. Your problem is calling the length width, and the width height, so let's use those terms.
P = W + W + H + H
or
P = 2W + 2H
We know the perimeter is 174, so we can write
2W + 2H = 164

Now we can use the information about the width and height to find another equation.
"Its width is 8 inches less than twice the height."
W = 2H - 8

Now you have a system of two equations.

2W + 2H = 164
W = 2H - 8

Solve the system of equations to find W.

Answer 2

here is a simple method

the sum of the length and width is 82

since the perimeter of a rectangle is P = 2(h + w)

so you can say 82 = h + w


let the height = h so the width is 2h - 8

then

82 = h + 2h - 8

or

82 = 3h - 8

solve for h, and you'll have the height... and can then calculate the width...

Answer 3

h=30

Answer 4

is the width 52?

Answer 5

Since all you are asked for is the width, you can solve the first equation for h, then substitute it in the second equation.

2W + 2H = 164
W = 2H - 8

Solve the first equation for H.
Divide both sides by 2:
W + H = 82
Subtract W from both sides:
H = 82 - W

Now substitute 82 - W for H in the second equation.

W = 2H - 8
W = 2(82 - W) - 8

Now solve for W.
W = 164 - 2W - 8

Answer 6

Correct.