Question

sara wants to fence in her triangular backyard. if she buys three pieces of wood measuring, 22 ft, 31 ft, 54 ft, will she have enough wood to build her triangular fence?
sara

enough wood to build her triangular fence, because the two smallest side measurements

to be larger than the third side.

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Let \(a = 22\), \(b=31\), \(c = 54\). We check \(a + b>c\).
\(a + b=22+31=53\)

Step2: Compare the sum with the third side

We have \(53<54\)

Answer:

Sara does not have enough wood to build her triangular fence, because the two smallest side measurements do not add up to be larger than the third side.