Question

Triangles ABC and XYZ are similar(pictured below). What is the perimeter 10 points of XYZ (Recall that the perimeter is the total distance around the shape). А Х с B Z 51 unite 21 units 25.5 unite 17 units None of the above

Answer 1

Given: The traingles given are similar to each other

This means that the ratios of similar sides can be taken and then used to obtain the missing sides

comparing similar sides

AB is similar to XY

BC is similar to YZ

AC is similar to XZ

Since we were given XZ = 9, we can find the other sides by comparing XZ with AC

`\frac{Triangle\text{ ZXY}}{\text{Triangle ABC}}\text{ =}(XZ)/(AC)=\text{ }(9)/(6)\text{ = 1.5}`

This shows that the sides of triangle ZYX are 1.5 times that of ABC

So that YZ = 1.5 x BC= 1.5 x 8 = 12,

YZ = 12

XY = 1.5 x AB= 1.5 x 3 = 4.5,

XY = 4.5

The sides are shown in the diagram below

The perimeter of the triangle XYZ = 9 + 4.5 + 12 = 25.5 units