Question

Triangle ABC is similar triangle XYZAB equals 12 a C equals 16 BC equals 20 and X equals 24 find the perimeter of XYZ

Answer 1

The perimeter of triangle XYZ is 96, found by calculating the scale factor using the lengths of similar triangles ABC and XYZ, then applying it to determine the remaining sides.

Step-by-step explanation:

The student has asked to find the perimeter of triangle XYZ which is similar to triangle ABC.

Given the lengths of sides AB, AC, and BC in triangle ABC as 12, 16, and 20 respectively, and side X in triangle XYZ as 24. Similar triangles have proportional sides, so we can find the scale factor and use it to determine the lengths of the other sides in triangle XYZ.

To find the scale factor (k), we compare the given sides of similar triangles: k = X / AB = 24 / 12 = 2.

Now that we know the scale factor, we can find the lengths of the remaining sides of triangle XYZ by multiplying the corresponding sides of triangle ABC by k.

So, we have:

• Length of YZ = k * AC = 2 * 16 = 32
• Length of XY = k * BC = 2 * 20 = 40

Finally, the perimeter of triangle XYZ is the sum of its sides: perimeter = X + YZ + XY

= 24 + 32 + 40

= 96.