Question

The perimeter of a triangle is 32 feet. One side of the triangle is 3 times the second side. The third side is 12 feet longer

Answer 1

We have a triangle whose perimeter is 32 feet. Some information regarding the sides of the triangle is given:

GiveN:

• One side is 3 times the second side.
• Third side is 12 feet longer than the second side.

As we can see that, two sides of the triangle are defined the second sides. It means First and third side can be expressed in the form of second side.

• So let the second side be x

Then,

• First side = 3x
• And, third side = x + 12

We know that, perimeters is the sum of the lengths of all sides of the triangle, So it can be written as:

$3x + x + x + 12 = 32$

Solving it further,

$5x + 12 = 32$

Subtracting 12 from both sides,

$5x + 12 - 12 = 32 - 12$

$5x = 20$

Dividing 5 from both sides,

$\frac{5x}{5} = \frac{20}{5}$

$x = 4$

Then,

• First side = 3x = 12 feet
• Second side = 4 feet
• Third side = x + 12 = 16 feet

And we are done with the answer !!

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