Question

In the triangle, x is 5 greater than y, and y is 21 less than three times z, and the perimeter is 180. What is the value of each variable? To find the answer, write a system of equations and use an inverse matrix to solve it. Please help, I don't understand.

Answer 1

x = 77

y = 72

z = 31

Explanation:

The formula for the Perimeter of triangle XYZ = x + y + z

From the question:

x + y + z = 180

In the triangle, x is 5 greater than y,

x = y + 5

y is 21 less than three times z

y = 3z - 21

3z = y + 21

z = y + 21/3

Hence:using substitution

x + y + z = 180

y + 5 + y + y/3 + 21/3 = 180

2y + y/3 + 5 + 21/3 = 180

2y + y/3 = 180 - ( 5 + 21/3)

2y + y/3 = 180 - (5 + 7)

2y + y/3 = 180 - 12

2y + y/3 = 168

Multiply both sides by 3

2y × 3 + y/3 × 3 = 168 × 3

6y + y = 504

7y = 504

y = 504/7

y = 72

Solving for x

x = y + 5

x = 72 + 5

x = 77

Solving for z

z = (y + 21)/3

z = (72 + 21)/3

z = 93/3

z = 31

Therefore,

x = 77

y = 72

z = 31