Question

A building in a city has a rectangular base. the length of the base measures 65 ft less than three times the width. the perimeter of this base is 870 ft. what are the dimensions of the​ base?

Answer 1

By setting up a system of equations with the given perimeter formula and dimensions relationship, we determine the dimensions of the rectangular base to be 310 ft by 125 feet.

Step-by-step explanation:

To determine the dimensions of a rectangular base where the length is 65 ft less than three times the width, and the perimeter is 870 ft, we can set up a system of equations. Let w represent the width of the rectangle, and l represent the length of the rectangle. From the problem, we have:

l = 3w - 65

Now, using the formula for perimeter of a rectangle (P = 2l + 2w), we can write:

870 = 2(3w - 65) + 2w

Solving for w, we find:

870 = 6w - 130 + 2w

870 + 130 = 8w

w = 1000 / 8

w = 125 feet

Substitute w back into the equation for l:

l = 3(125) - 65

l = 375 - 65

l = 310 feet

Therefore, the dimensions of the building are 310 ft by 125 feet.

Answer 2

Call the length is x
the width is y

First equation:

`3y - x = 65`

Simplized the equation:

`- x + 3y = 65`

Second equation:

`(x + y) * 2 = 870`
Simplized the equation:

`x + y = 435`
from two equation we have:

`- x + 3y = 65 \\ x + y = 435`
Use Eliminate Method:

`4y = 500 \\ x + y = 435`

`y = 125 \\ x + 125 = 435`

`y = 125 \\ x = 310`
Conclude:
The length is 310 feets
The width is 125 feets