Question

A building in a city has a rectangular base. The length of the base measures 70 feet less than three times the width. The perimeter of this base is 860 feet. What are its dimensions of the base?

Answer 1

information that we have

Width --> I will call the width "x"

Length ---> Since the length is 70 less than 3 times the width, that means the length is: "3x-70"

In summary:

$\begin{gathered} WIDTH=x \\ \text{LENGTH}=3x-70 \end{gathered}$

We know that the perimeter of the base is:

$PERIMETER=860ft$

Next, we use the formula for perimeter, which is:

$PERIMETER=2\times LENGTH+2\times\text{WIDTH}$

And we substitute the values that we have for perimeter, length and width:

$860=2(3x-70)+2x$

We need to solve this equation for x to be able to find the dimensions.

-Use distributive property to multiply 2 by 3x and by -70:

$860=6x-140+2x$

Combine like terms (the two terms with x on the right side):

$860=8x-140$

Add 140 to both sides of the equation:

$\begin{gathered} 860+140=8x-140+140 \\ 1000=8x \end{gathered}$

Next we divide both sides by 8: