Question

I will give you 95 points for this! The figure shows two right triangles, each with its longest side on the same line.

Answer 1

• See below

Explanation:

We have similar triangles:

• ΔXYZ ~ ΔRST

The reason is:

• The long sides lie on the same line
• Other sides are vertical and horizontal, so the corresponding sides are parallel to each other
• These give us the AA similarity

The slope is:

• m = rise / run

According to the ΔRST the slope is:

• m = 2/4 = 1/2

Find the length of XY, using the ratio of corresponding sides:

• XY / RS = YZ / ST
• XY = RS * YZ / ST = 4*3/2 = 6 units