The area of the rectangle in square units

Question

A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 units, what is the area of the rectangle in square units?

A) 36

B) 48

C) 72

D) 96

monkey mart

Answer 1

Perimeter is 2W + 2L = P

Area is LW = A

L = 3W (given)

P = 48 (given)

48 = 2W + 2(3W) (substitution of 3W for L)

48 = 2W + 6W = 8W

W = 48/8 = 6 units

Then L = 3(6) = 18 units.

Check: 2(6) + 2(18) = 12 + 36 = 48 units

Area = 18(6) = 108 sq units (not an answer choice !!??)

Answer 2

Area = 108 units^2

L =3w

P=48 = 2L+2w

24 = L+w = 3w+w = 4w

w = 24/4 =6

L =3(6) = 18

A = 18(6) 108 square units = Area

Answer 3

Check this illustrated solution: https://pdfarrell1.github.io/Rectangle-Problem-Solution/

Answer 4

I think the value on this one would actually be something that is not listed as an answer choice! Haha, did it give you like a fill in the blank option or something like that?

In terms of the solving what you want to do is set up a general equation for the Perimeter and Area. For this one that would be

Perimeter = 2 * (length + width)

Area = length x width

Since we know that l = 3w from the information in the question you can substitute to get

P = 2(3w + w) = 8w

Setting equal to 48 means that 8w = 48

So w = 6 and l = 3 x 6 = 18

Putting that all together then would give an Area value of

Area = 18 x 6 = 108

I hope that helps get you moving in the right direction! Feel free to reach out if you have any more questions beyond that :)

Answer 5

Perimeter of a rectangle = 2(l + w) = 48

l + w = 24

Known: l = 3w

Substitute: 3w + w = 24

4w = 24

w = 6 units

Substitute: l + 6 = 24

l = 18 units

Area of a rectangle = lw = (18 units)(6 units) = 108 units²

The answer is that the area of the rectangle is 108 units² which is not any of the provided answer choices. An important thing to keep in mind are the units. Since you are calculating an area, the units are represented as the square of a distance.