Applications, Distance, and Midpoint

Question

The shortest side of a right triangle is 3 miles long. The difference between the lengths of the other two sides is 1 mile. Find the missing sides. Use exact values.

Long leg : _____miles

hypotenuse:____  miles

Answer 1

The hypotenuse must be longer than either of the legs. So the differnce between the hypotenuse and the middle leg is 1.

So hypotenuse = (x+1)² = x² + s², where s is the length of the shortest leg.

Thus, x² + 2x + 1 = x² + s².

So, 2x + 1 = s² = 3² = 9.

2x + 1 = 9

Subtracting 1 from both sides,

2x = 8

Divide both sides by 2:

x = 4.

The hypotenuse must be x +1 = 4 + 1 = 5.

The given units are always miles.