Question

devon reseeded a section of lawn that he plans to protect by putting a fence around it. 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 section of lawn. devon choose... enough fencing for this project.

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

Step3: Compare with available fencing

Devon has 55 feet of fencing. Since \(55<60\), he does not have enough.

Answer:

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