Question

The ratio of the measures of the sides of a triangle is 3:4:5. Its perimeter is 48 inches. Find the scale factor as a decimal, and the measure of each side of the triangle.

Answer 1

The scale factor is 4.

Sides are 12 inches, 16 inches, 20 inches.

Explanation:

The ratio is 3 : 4 : 5 and the perimeter is 48 inches.

Let the scale is p.

The length of sides is 3 p , 4 p and 5 p.

So, the perimeter is

3 p + 4 p + 5 p = 48

12 p = 48

p = 4

So, the scale factor is 4.

Sides are 12 inches, 16 inches, 20 inches.

Answer 2

Given:

The ratio of the measures of the sides of a triangle is 3:4:5.

Its perimeter is 48 inches.

To find:

The scale factor as a decimal, and the measure of each side of the triangle.

Solution:

Let x be the scale factor. Then the measures of sides of the triangle are 3x, 4x and 5x.

The perimeter of the triangle is 48 inches. It means the sum of all sides of the triangle is 48 inches.

`3x+4x+5x=48`

`12x=48`

Divide both sides by 12.

`x=(48)/(12)`

`x=4`

Now, the measures of sides are:

`3x=3(4)`

`3x=12`

Similarly,

`4x=4(4)`

`4x=16`

And,

`5x=5(4)`

`5x=20`

Therefore, the scale factor is 4 and the measures of sides are 12, 16 and 20.