Question

the hypotenuse of the right triangle is 5y inches long. the lengths of the legs are x + 8 and x + 3 inches. if the perimeter of the triangle is 76 inches and the length of the hypotenuse minus the length of the shorter leg is 17 inches, how many inches long is the hypotenuse?
hint 1: (x + 8) + (x + 3) + (5y) = 76 and (5y) - (x + 3) = 17
hint 2: be sure to find the value of what you are asked to solve.
a) 35
b) 15
c) 10

Explanation:

Step1: Simplify the perimeter equation

The perimeter equation is \((x + 8)+(x + 3)+(5y)=76\). Combine like terms: \(2x+5y + 11=76\), so \(2x+5y=65\) (Equation 1).

Step2: Simplify the hypotenuse - shorter leg equation

The other equation is \((5y)-(x + 3)=17\). Simplify it: \(5y-x-3 = 17\), so \(5y-x=20\) (Equation 2).

Step3: Solve the system of equations

From Equation 2, we can express \(x\) in terms of \(y\): \(x = 5y-20\). Substitute this into Equation 1:
\(2(5y - 20)+5y=65\)
\(10y-40 + 5y=65\)
\(15y=105\)
\(y = 7\).

Step4: Find the hypotenuse length

The hypotenuse is \(5y\) inches long. Substitute \(y = 7\) into \(5y\): \(5\times7 = 35\).

Answer:

A) 35