PLEASE HELP. WILL GIVE BRAINLIEST. :)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 inchesb. 3.7 inchesc. 4.2 inchesd. 4.4 inches

Accepted Solution

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
SolutionPR=3.7 inches; CR=5.6 inches; AC=4.9 inchesAs the two triangles QRP and ARC are similar, their sides must be proportionals, then:PQ/AC=PR/CR=QR/ARReplacing the given values in the proportion above:PQ/(4.9 inches)=(3.7 inches)/(5.6 inches)=QR/ARPQ/(4.9 inches)=3.7/5.6Solving 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 inchesPQ=18.13/5.6 inchesPQ=3.2375 inchesRounding to one decimal place:PQ=3.2 inches