Answer:
4 inches and 3 inches.
Step-by-step explanation:
In a right triangle, the hypotenuse is equivalent to the sum of the square of both legs, or "Pythagorean Theorem" with the formula of: c² = a² + b², where c stands for "hypotenuse" while a and b stands for both legs.
If the hypotenuse measures 5 inches, and the measure of the shorter leg is 1 less than the measure of the longer leg, then:
Note: a = longer leg. If the shorter leg is 1 less than the measure of the longer leg, then the measure of the shorter leg is a - 1.
5² = a² + (a - 1)²
25 = a² + (a² - 2a + 1)
25 = a² + a² - 2a + 1
25 = 2a² - 2a + 1
25 - 1 = 2a² - 2a
24 = 2a² - 2a
(24)/2 = (2a² - 2a)/2
12 = a² - a
0 = a² - a - 12
0 = (a - 4)(a - 3)
0 = a - 4; 0 = a - 3
4 = a; 3 = a
Thus, the measure of the longer leg is 4 inches, while the measure of the shorter leg is 3 inches.
