Question

Whats the answer- the second side of a triangular deck is 4 feet longer than the shortest​ side, and the third side is 4 feet shorter than twice the length of the shortest side. if the perimeter of the deck is 52 ​feet, what are the lengths of the three​ sides?

Answer 1

Let's assume x be the shortest side of the triangle.

Given that, the second side of a triangular deck is 4 feet longer than the shortest​ side. So,

Second side = 4 + x.

And the third side is 4 feet shorter than twice the length of the shortest side.

So, third side = 2x - 4.

The perimeter of the deck is 52 ​feet. Perimeter is the sum of all sides of a triangle.

So, we can set up an equation as following:

x +4 + x + 2x - 4 = 52

4x = 52 Combine the like terms.

`(4x)/(4) =(52)/(4)` Divide each sides by 4 to isolate x.

So, x = 13.

Hence, the shortest side = 13.

Now the second side = 4 + x = 4 + 13 = 17

And third side = 2x - 4 = 2(13) - 4 = 26 - 4 = 22

Hence the three sides of the triangle are 13 feet, 17 feet, and 22 feet.

Hope this helps you!.