Question

A triangle has a perimeter of 48 inches. Side B is nine inches longer than side A. The base is 7 inches more than twice side A. What are the dimensions of the triangle?

Answer 1

(A, B, C) = (8, 17, 23) inches

Explanation:

We can let A, B, and C represent the corresponding side lengths. Then we are given ...

A + B + C = 48 . . . . . . the perimeter is 48 inches

B = A + 9 . . . . . . . . . . . B is 9 inches longer than A

C = 2A +7 . . . . . . . . . . the base (remaining side) is 7 inches more than ...

Substituting for B and C in the first equation, we have ...

A + (A+9) +(2A+7) = 48

4A = 32 . . . . . . . . . . . . . . collect terms, subtract 16

A = 8

B = A+9 = 17

C = 2A +7 = 23

Side A is 8 inches, side B is 17 inches, and side C is 23 inches.