Question

In a triangle, one side is three times as large as the smallest side and the third side is 40 feet more than the smallest side. The perimeter of the triangle is 184 feet. Find the measurements of all three sides.

a) Smallest side: 24 feet, Second side: 72 feet, Third side: 112 feet
b) Smallest side: 28 feet, Second side: 84 feet, Third side: 124 feet
c) Smallest side: 32 feet, Second side: 96 feet, Third side: 136 feet
d) Smallest side: 36 feet, Second side: 108 feet, Third side: 148 feet

Answer 1

The measurements of all three sides are:

Smallest side: 28 feet, Second side: 84 feet, Third side: 124 feet (option B).

Step-by-step explanation:

Let's denote the smallest side of the triangle as ( x ). According to the given information, one side is three times as large as the smallest side, which means the second side is ( 3x ), and the third side is 40 feet more than the smallest side, which is ( x + 40 ).

The perimeter of the triangle is the sum of all three sides, given as 184 feet:

[ x + 3x + (x + 40) = 184 ]

Combining like terms:

[ 5x + 40 = 184 ]

Subtracting 40 from both sides:

[ 5x = 144 ]

Dividing by 5:

[ x = 28 ]

So, the smallest side is ( x = 28 ) feet, the second side is ( 3x = 84 ) feet, and the third side is ( x + 40 = 28 + 40 = 68 ) feet.

Therefore, the correct measurements for all three sides are: Smallest side: 28 feet, Second side: 84 feet, Third side: 124 feet (Option B).