Question

The figure below shows the storage space under a stairway in Nina’s house.

A right triangle PQR with right angle at R and QR as the base. RX meets PQ at X at a right angle. The length of the segment QX is 3.6 feet. The length of the hypotenuse PQ is 10 feet.

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

Can you first figure out the length of PX?

Answer 2

6.4

Answer 3

Alright.
\[\frac{PX}{RX} = \frac{RX}{QX}\]Do you know how to solve proportions?

Answer 4

Cross multiply?

Answer 5

Yes.\(\space\large\frac{6.4}{x} = \frac{x}{3.6}\space\)which is the same as \(x^{2} = 23.04\)

Answer 6

Solve for x.

Answer 7

then square root it?

Answer 8

Yeah.

Answer 9

so x=4.8ft