Perimeter of a plot. Do not understand. Help!

Question

The perimeter of a plot of land in the shape of a right triangle is 48 miles. If the length of one leg of the triangle exceeds the other leg by 4 miles, find the length of each boundary of the land.

the lengths of the boundaries of the land are __,__,__ miles.

there are three answers to this question. I have been working on these questions and it don’t make sense. Appreciate the help!

Answer 1

Here are some hints.

If one leg is x, the other leg is x+4, then the hypotenuse can be represented by 48-(2x+4)=44-2x.

Now by the Pythagorean Theorem x² + (x+4)² = (44-2x)².

So, square the two binomials, set equal to zero (combining similar terms) and solve by factoring, completing the square, or the quadratic formula. One of the answers for x (80) will have to be rejected because it is larger than the given perimeter.

See if you can take it from there.