Question

The perimeter of a triangle is 56 inches. The longest side measures 4 inches less than the sum of the other two sides. Three times the shortest side is 4 inches more than the longest side. Find the lengths of the three sides of the triangle.

A. Shortest side: 14 inches, Intermediate side: 22 inches, Longest side: 20 inches
B. Shortest side: 22 inches, Intermediate side: 14 inches, Longest side: 20 inches
C. Shortest side: 14 inches, Intermediate side: 20 inches, Longest side: 22 inches
D. Shortest side: 20 inches, Intermediate side: 14 inches, Longest side: 22 inches

Answer 1

To find the lengths of the three sides of the triangle, set up a system of equations and solve them simultaneously. The correct answer is option D: Shortest side: 20 inches, Intermediate side: 14 inches, Longest side: 22 inches.

Step-by-step explanation:

To find the lengths of the three sides of the triangle, we can set up a system of equations. Let's denote the lengths of the three sides as x, y, and z. From the given information, we have the following equations:

x + y + z = 56 (perimeter of the triangle)

z = x + y - 4 (longest side is 4 inches less than the sum of the other two sides)

3x = z + 4 (three times the shortest side is 4 inches more than the longest side)

Solving these equations simultaneously, we can find the values of x, y, and z. The correct answer is option D: Shortest side: 20 inches, Intermediate side: 14 inches, Longest side: 22 inches.