Question

The figure below shows the storage space under a stairway in Nina’s house.
Nina plans to utilize the storage space and make shelves. She wants to fix a wood beam, represented by segment RX in the figure, to support a shelf.

What is the length of the beam? Show all the steps you used to find your answer.

Answer 1

\(\triangle PXR \sim \triangle RXQ\)

Answer 2

setup an useful proportion

Answer 3

before setting up the proportion,
see that PX = 10-3.6
= 6.4

Answer 4

\(\large \frac{RX}{PX} = \frac{QX}{RX}\)

Answer 5

cross multiply

Answer 6

\(\large RX^2 = QX \times PX \)

Answer 7

lol alright

Answer 8

plugin QX, PX values

Answer 9

wait can what are the values for the variables? so i can solve the proportion

Answer 10

look at the figure

Answer 11

QX = ?
PX = ?

Answer 12

10 for Qx?

Answer 13

px 6.4?

Answer 14

10 for QX ??? look closer

Answer 15

QX = 3.6
PX = 6.4

Answer 16

plug them

Answer 17

\(\large RX^2 = QX \times PX \)

\(\large RX^2 = 3.6 \times 6.4\)

Answer 18

multiply and take square root

Answer 19

4.8?

Answer 20

looks correct !

Answer 21

so can i use all the steps you gave to to explain how i got the length of the beam? :)

Answer 22

yes !