Question

the section of lawn is in the shape of a right triangle with a leg that is 10 feet long and a hypotenuse that is 26 feet long.

devon has 55 feet of fencing. does devon have enough fencing for this project? use the drop - down menus to explain.

click the arrows to choose an answer from each menu.

first, find the missing side length of the triangle, x, by solving choose... . then use the value of x to calculate that choose... feet of fencing is needed for the triangular

Explanation:

Step1: Find the missing leg

In a right triangle, we use the Pythagorean theorem: \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse, and \(a\), \(b\) are the legs. Let one leg \(a = 10\), hypotenuse \(c=26\), and the other leg be \(x\). So we solve \(10^{2}+x^{2}=26^{2}\).
\[

$$\begin{align*} 100 + x^{2}&= 676\\ x^{2}&=676 - 100\\ x^{2}&= 576\\ x&=\sqrt{576}\\ x& = 24 \end{align*}$$

\]

Step2: Calculate the perimeter

The perimeter \(P\) of the right triangle is the sum of all three sides: \(P=10 + 24+26\).
\[
P=10 + 24+26=60
\]

Step3: Compare with 55

Since \(60>55\), Devon does not have enough fencing.

Answer:

First, find the missing side length of the triangle, \(x\), by solving \(10^{2}+x^{2}=26^{2}\) (which gives \(x = 24\)). Then use the value of \(x\) to calculate that \(60\) feet of fencing is needed for the triangular lawn. Since \(60>55\), Devon does not have enough fencing.