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in a right triangle, the hypotenuse measures 5inches. If the measure of the shorter leg is 1 less than the measure of the longer leg, how long is each leg?

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Sagot :

JJMathLoveridn

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.

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