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

Using the Pythagorean theorem \(a^2 + b^2 = c^2\), where \(c = 26\) (hypotenuse) and \(a = 10\) (one leg). Let the missing leg be \(x\). So \(10^2 + x^2 = 26^2\), which simplifies to \(100 + x^2 = 676\). Then \(x^2 = 676 - 100 = 576\), so \(x = \sqrt{576} = 24\).

Step2: Calculate the perimeter

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

Step3: Compare with available fencing

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

Answer:

First, solve \(10^2 + x^2 = 26^2\) to find \(x = 24\). Then, the perimeter is \(10 + 24 + 26 = 60\) feet. Devon does not have enough fencing.