Question

The 2 triangles are similar. if the perimeter of triangle abc is 28, find the value of x​

Answer 1

To find the value of x in the similar triangles ABC and XYZ, we need to use the fact that the ratio of their corresponding sides is the same. By setting up an equation using the perimeter of triangle ABC and substituting the known value of AB, we can solve for x.

Step-by-step explanation:

To find the value of x, we need to use the fact that the two triangles ABC and XYZ are similar. Since they are similar, the ratio of their corresponding sides is the same. Let's say the ratio is k. This means that:

AB/XY = BC/YZ = AC/XZ = k

Given that the perimeter of triangle ABC is 28, we can write: AB + BC + AC = 28

Using the ratio k, we can rewrite this equation as: kXY + kYZ + kXZ = 28

Since we know that AB = 3x, we can substitute this in the equation: 3kXY + 3kYZ + 3kXZ = 28

Simplifying, we have: kXY + kYZ + kXZ = 28/3

Therefore, the value of x is 28/9.75.

Answer 2

given the sides 8 and 10 are similar we can assume that triangle abc is 80% as large. meaning the perimeter of triangle rst is 35.
so 10 + x - 4 + x - 1.5 = 35
4.5 + 2x = 35
2x = 30.5
x = 15.25