Question

Two triangles are similar. The sides of the first triangle are 8,10 and 12. The smallest side of the second triangle is 24. Find the perimeter of the second triangle.

Answer 1

so 8*3=24, so multiply all of the sides by 3,
the other 2 are 30 and 36

Answer 2

The perimeter of the second triangle is 90 units.

What are similar figures?

Similar figure are zoomed in or zoomed out (or just no zoom) version of each other. They are scaled version of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.

So, if a side of a figure is of length L units, and that of its similar figure is of M units, then:

$L = k \times M$  

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

For this case, the two considered triangles are similar. Thus:

A side of first triangle = k times corresponding side of its similar triangle

where k is the scale factor, constant for one pair of similar triangles.

We're given that:

Sides of first triangle are of 8,10 and 12 unit length.

Smallest side of second triangle is of 24 units.

Now, smallest side of first triangle will correspond to the smallest side of its similar triangle.

For first triangle, the smallest side is of 8 units (8 is smaller than 10 and 12, the other two sides).

Let the sides of second triangle be of S = 24 units, M units, and L units.

where M is middle sized side and L is largest side of second triangle.

Let the scale factor be 'k'.

Then, we get:

Smallest side of first triangle = k × smallest side of its similar triangle

$8 = k \times 24\\\\k = \dfrac{8}{24} = \dfrac{1}{3}$

Similarly, middle sized side of first triangle = (1/3) × middle sized side of second triangle

$10 = k \times M = \dfrac{1}{3} \times M\\\\M = 3 \times 10 = 30$units.

Thus, the length of middle sized side of second triangle is 30 units.

Largest side of first triangle = (1/3) × Largest side of second triangle

$12 = k \times L = \dfrac{1}{3} \times L\\\\L = 3 \times 12 = 36$units.

Thus, the length of middle sized side of second triangle is 30 units.

Perimeter of the second triangle = sum of length of its sides

=  S + L + M =  24 + 30 + 36 = 90 units.

Thus, the perimeter of the second triangle is 90 units.

Learn more about scale factor here:

https://brainly.com/question/8765466