Answer:
Explanation:
Let x represent the length of the hypotenuse.
Let y represent the length of the the shorter leg.
Let z represent the length of the longer leg.
The length of the longer leg of a right triangle is 20 inches more than twice the length of the shorter leg. It means that
z = 2y + 20
The length of the hypotenuse is 22 inches more than twice the length of the shorter leg. It means that
x = 2y + 22
We would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
(2y + 22)² = y² + (2y + 20)²
(2y + 22)(2y + 22) = y² + (2y + 20)(2y + 20)
= 4y² + 44y + 44y + 484 = y² + 4y² + 40y + 40y + 400
4y² + 88y + 484 = y² + 4y² + 80y + 400
4y² + 88y + 484 = 5y² + 80y + 400
5y² - 4y²+ 80y - 88y + 400 - 484
y² - 8y - 84 = 0
y² + 6y - 14y - 84 = 0
y(y + 6) - 14(y + 6)
y - 14 = 0 or y + 6 = 0
y = 14 or y = - 6
The shorter length cannot be negative hence y = 14 inches
The length of the shorter side is 14 inches.
The length of the hypotenuse is
(2 × 14) + 22 = 50 inches
The length of the longer side is
(2 × 14) + 20 = 48 inches