A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 23 feet more than the length of the shortest side. If the perimeter is 167, what are the three sides?

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Answer 1 · 2017-02-02T10:57:30

The three sides are $36 f t$ $36ft$ , $72 f t$ $72ft$ and $59 f t$ $59ft$ .

Let the length of the shortest side of the triangular flower bed be $x$ $x$ feet.

Then the length of the second side is $2 x$ $2x$ and

the length of the third side is $x + 23$ $x +23$

The given perimeter is $167 f t$ $167ft$ hence:

$x + 2 x + x + 23 = 167$ $x+2x+x+23=167$

$4 x + 23 = 167$ $4x+23=167$

$4 x = 167 - 23$ $4x=167-23$

$4 x = 144$ $4x=144$

$x = \frac{144}{4} = 36$ $x=144/4=36$

$2 x = 2 \cdot 36 = 72$ $2x=2*36=72$

$x + 23 = 36 + 23 = 59$ $x+23=36+23=59$

The length of the three sides of the triangular flower bed are $36 f t$ $36ft$ , $72 f t$ $72ft$ and $59 f t$ $59ft$ .