Question

The length of one leg of the right triangle is 2 ft less than the length of the hypotenuse. The length of the other leg is 1 ft less than the length of the hypotenuse. Find the length of the sides.

Answer 1

Answer:

The length of the sides are 3 feet and 4 feet, respectively.

Step-by-step explanation:

Given the fact that triangle is a right triangle, it can be represented by Pythagorean Theorem:

$r^{2} = x^{2}+y^{2}$

Where:

$r$ - Hypotenuse, measured in feet.

$x$, $y$ - Legs, measured in feet.

In addition, each leg can be determined as functions of hypotenuse:

$x = r-2\,ft$

$y = r-1\,ft$

Hence, the Pythagorean identity can be expanded and remaining variable may be solved:

$r^{2} = (r-2\,ft)^{2}+(r-1\,ft)^{2}$

$r^{2} = r^{2}-4\cdot r +4 + r^{2}-2\cdot r +1$

$r^{2}-6\cdot r +5 =0$

$(r-5)\cdot (r-1) = 0$

$r = 5\,ft\,\vee\,r = 1\,ft$

According to the definition of hypotenuse, it must be longer than any of legs. Hence, there is just one solution that is reasonable:

$r = 5\,ft$

And length of the sides are, respectively:

$x = 5\,ft-2\,ft$

$x =3\,ft$

$y = 5\,ft-1\,ft$

$y = 4\,ft$

The length of the sides are 3 feet and 4 feet, respectively.