Question

What is the value of x?

12 units
15 units 20 units
25 units

Answer 1

A: 12 units

Explanation:

on edge! hope this helps!!~ ≧(´▽｀)≦

Answer 2

12 units

Explanation:

All of the right triangles in this figure are similar, so corresponding sides have the same ratio.

short side / long side = 9/x = x/16

x^2 = 144 . . . . . cross multiply

x = √144 = 12

The value of x is 12 units.

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Comment on this geometry

The value of x is the "geometric mean" of 9 and 16. That is ...

RT = √(ST·QT)

There are other geometric mean relationships in this figure as well, all of which derive from the fact the triangles are similar.

RS = √(TS·QS)

RQ = √(TQ·SQ)