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 side length

Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a,b\) are the legs. Let \(a = 10\), \(c=26\), and \(b=x\). Then \(x^{2}+10^{2}=26^{2}\), so \(x^{2}=26^{2}-10^{2}\).

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Step2: Calculate the perimeter

The perimeter \(P\) of a triangle is \(P=a + b + c\). Substituting \(a = 10\), \(b=24\), and \(c = 26\), we get \(P=10+24 + 26=60\)

Answer:

First, find the missing side length of the triangle, \(x\), by solving \(x^{2}+10^{2}=26^{2}\). 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.