Question

The length of one side of a triangle is 2 feet less than three times the length of its second side. The length of the third side is 3/4
of the sum of the lengths of the first two sides. Find the lengths of all three sides if the perimeter of the triangle is 17.5 feet.


P=17.5 feet

Answer 1

Using a system of equations, it is found that the lengths of the sides of the triangle are given as follows:

0.91 feet, 0.73 feet, 1.23 feet.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are the lengths, given by x, y and z.

The length of one side of a triangle is 2 feet less than three times the length of its second side, hence:

y = 3x - 2.

The length of the third side is 3/4 of the sum of the lengths of the first two sides, hence:

$z = \frac{3(x + y)}{4} = \frac{3(4x - 2)}{4}$

The perimeter of the triangle is 17.5 feet, hence:

$x + y + z = 17.5$

$x + 3x - 2 + \frac{3(4x - 2)}{4} = 17.5$

$4x + \frac{3(4x - 2)}{4} = 19.5$

$16x + 12x = 25.5$

x = 25.5/28

x = 0.91.

Then the other sides are:

• y = 3x - 2 = 3(0.91) - 2 = 0.73 feet.

• $z = \frac{3(4 x 0.91 - 2)}{4} = 1.23 feet$

More can be learned about a system of equations at brainly.com/question/24342899

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