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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 3.7 inches, and the length of segment CR is 5.6 inches. The distance between A and C is 4.9 inches.

What is the distance between the endpoints of the beams P and Q?

a. 3.2 inches
b. 3.7 inches
c. 4.2 inches
d. 4.4 inches

Question

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Professor1994 Professor1994 · Answer 1 · 2018-11-13T23:31:57+01:00

Answer: Using the proportion beteween the sides of the similar triangles, the distance between the endpoints of the beams P and Q is 3.2 inches.

Option a. 3.2 inches

Solution

PR=3.7 inches; CR=5.6 inches; AC=4.9 inches

As the two triangles QRP and ARC are similar, their sides must be proportionals, then:

PQ/AC=PR/CR=QR/AR

Replacing the given values in the proportion above:

PQ/(4.9 inches)=(3.7 inches)/(5.6 inches)=QR/AR

PQ/(4.9 inches)=3.7/5.6

Solving for PQ: Multiplying both sides of the equation by 4.9 inches:

(4.9 inches)[PQ/(4.9 inches)]=(4.9 inches)(3.7/5.6)

PQ=(4.9)(3.7)/5.6 inches

PQ=18.13/5.6 inches

PQ=3.2375 inches

Rounding to one decimal place:

PQ=3.2 inches

eudora eudora · Answer 2 · 2019-04-29T20:09:36+02:00

Answer:

Option A. 3.2 inches

Step-by-step explanation:

As shown in the figure it is given that Δ QRP and Δ ARC are two similar triangles.

Given lengths are mPR = 3.7 inches

mCR = 5.6 inches

Distance between A and C is = 4.9 inches

By the theorem of similar triangles in Δ PQR and Δ ACR

[tex]\frac{PQ}{AC}=\frac{PR}{RC}[/tex]

[tex]\frac{PQ}{4.9}=\frac{3.7}{5.6}[/tex]

[tex]PQ=\frac{(4.9)(3.7)}{(5.6)}=\frac{18.13}{5.6}=3.2[/tex]

Therefore Option A. mPQ = 3.2 inches is the answer