Joshua used two wood beams, PC and QA, to support the roof of a model house. The beams intersect each other to form two similar triangles QRP and ARC as shown in the figure below. The length of segment PR is 3.4 inches and the length of segment CR is 5.1 inches. The distance between A and C is 4.2 inches.

Question

anonymous · Answer

attachment

anonymous · Answer

what is the distance between the endpoints of the beams P and Q

ash2326 · Answer

Do you know the properties of similar triangles?

anonymous · Answer

They have identical angles and lengths

ash2326 · Answer

Identical Angles --->Yes
Not identical sides
They have sides in the same ratio. If sides and angles both are equal, then the triangles are congruent.

ash2326 · Answer

triangle PQR similar to triangle CAR so
$$\frac{PR}{CR}=\frac{PQ}{CA}$$
Do you get this?

anonymous · Answer

yes

ash2326 · Answer

Plugin the values given
$$\frac{3.4}{5.1}=\frac{PQ}{4.2}$$
Can you find the value of PQ from here?

anonymous · Answer

x over 5.1= x over 4.2 right?

ash2326 · Answer

how did you get this?

anonymous · Answer

So then you cross multiply and and then divide?

ash2326 · Answer

yes

anonymous · Answer

Thank You

ash2326 · Answer

welcome :)