Question

A rectangle is 3 times as long as it is wide. The perimeter id 70 cm. Findthe dimensions of the rectangle. Round to the nearest tenth if necessary.

Answer 1

If its 3 times as long as wide then

L = 3w (Equation 1)

The formula for perimeter is:

2L + 2w = P

We cal get rid of the L by replacing it with 3w, as we showed L=3w in Equation 1

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

We know the perimeter is 70 so lets plug that in and simplify the equation:

6w+2w=70

8w=70

Solve for w and you get w=8.75 cm

Now plug our value for w into equation 1:

3(8.75)=L

L=26.25 cm

Round to the nearest tenth gives our dimensions as:

8.8 cm x 26.3 cm

Answer 2

From what the problem tells us, we can set up an equation and solve for x:

`2x + 2(3x) = 70\\2x + 6x = 70\\8x = 70\\x = 8.75`

Then, we solve for the dimensions:

`w = 8.75\\l = (8.75)*3\\l = 26.25`

Then, check our work to confirm the dimensions yield the correct perimeter:

`2(8.75) + 2(26.25) = 70`