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? (6 points)

3.2 inches
3.7 inches
4.2 inches
4.4 inches

a

step-by-step explanation:

the answer is d

step-by-step explanation:

you can also use mathway to get you answer + steps

i believe a. 12x≥120 is the answer

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough