Question

The area of a rectangular glass slab is 80 square centimeters and its perimeter is 36 centimeters. If the length and width of the frame are multiplied by 4, what will be the perimeter of the new frame?
Select one:
a. 144 cm
b. 141 cm
c. 99 cm
d. 124 cm

Answer 1

First, you have to find out the values of the length and width.

Let l = length and w = width.

Set up your equation for area: l * w = 80

Set up your equation for perimeter: 2l + 2w = 36

We can use substitution for this problem, so find out the value of l or w. In this case, I will use the first equation to find out the value of l.

(Divide w on both sides) l = 80 / w

Since I know that l = 80 / w, I can substitute it into the second equation.

2l + 2w = 36, and l = 80 / w

= 2 (80/w) + 2w = 36

Simplify the equation.

= 160/w + 2w = 36

Get rid of the w in the denominator by multiplying the entire equation by w.

= ( 160/w + 2w = 36 ) * w

= 160 + $2w^{2}$ = 36w

= 2 ( w - 8 ) ( w - 10 )

The solutions for width (w) is 8 or 10. Then, you can use both 8 and 10 as your length and width, either or is fine. Multiply by 4 for each of those values and you get 8 x 4 = 32 and 10 x 4 = 40. The new perimeter would be 2(32) + 2(40) =

a. 144 cm

Hope this helped you! Let me know if there are any confusions :)