The perimeter of a triangle is 110 feet.The longest side of the triangle is 21 feet longer than the shortest side.The sum of the lengths of the two shorter sides is 12 feet more than the length of the longest side.Find the lengths of the sides of the triangle.
A)50 ft,33 ft,28 ft
B)49 ft,34 ft,28 ft
C)49 ft,33 ft,50 ft
D)49 ft,33 ft,28 ft
E)49 ft,35 ft,28 ft

Question

The perimeter of a triangle is 110 feet.The longest side of the triangle is 21 feet longer than the shortest side.The sum of the lengths of the two shorter sides is 12 feet more than the length of the longest side.Find the lengths of the sides of the triangle. ​
A)50 ft,33 ft,28 ft
B)49 ft,34 ft,28 ft
C)49 ft,33 ft,50 ft
D)49 ft,33 ft,28 ft
E)49 ft,35 ft,28 ft

Quizplus · Accepted Answer

Let x be the length of the shortest side, then the longest side is x+21 and the sum of the two shorter sides is (x+x+21) = 2x+21. We know that the perimeter is 110, so:

x + (x+21) + (2x+21) = 110
4x + 42 = 110
4x = 68
x = 17

Therefore, the length of the longest side is x+21 = 38 and the remaining side is 2x+21 = 55. The lengths of the sides are 17 ft, 38 ft, and 55 ft.

The only answer choice that matches this is D.

The Perimeter of a Triangle Is 110 Feet