The perimeter of a triangle is 166 inches. Side x is three times the length of the Side z. Side x is also 34 inches more than one-half the sum Sides y and z. Find the length of each side.

Answer 1

Perimeter = 166

Equation 1: X = 3z

Equation 2: X = 0.5(y+z) + 34

We are tole nothing about side y, but we know that

Equation 3: x+ y + z = 166

This is a system of 3 equations in 3 variables. My strategy would be to substitute Equation one into Equations 2 and 3.

3z = 0.5(y+z) + 34 and 3z + y + z = 166

Simplifying

3z = 0.5y + 0.5z +34. 4z +y = 166

2.5z - 0.5y = 34

New system

4z+y=166

2.5z -0.5y= 34

now use elimination to cancel y, multiply the top Equation by 0.5

2z + 0.5y= 83 , add this to the bottom Equation

2z + 0.5y = 83

2.5z -0.5y = 34

4.5z = 117

Z= 26

With z known, go back and find y and then X

4z + y = 166. Plug in z = 26

4(26) + y = 166

104 + y = 166. So y = 62

Now find X

X + y + z = 166. Y = 62 and z = 26

X + 62 + 26= 166

X = 78

X= 78

Y=62

Z= 26