find area of square????

Answers
Step-by-step explanation:
A triangle with sides AB = 3, BC = 4, and AC = 5 has an inscribed square PQRS with side QR along the side AC. What is the area of the square?
Because ABC is a 3-4-5 triangle, it is a right triangle.
Consequently, triangles ABC, PBS, SRC, and AQP are similar triangles. In each triangle, the longer leg to the shorter leg has a ratio of 4/3 (and the shorter leg to longer leg is a ratio of 3/4).
Suppose the square has a side length equal to s. Then QR = s. In triangle SRC, SR = s, so RC = (4/3)s. In triangle AQP, PQ = s, so AQ = (3/4)s.
Thus we have:
AC = AQ + QR + RC
AC = (3/4)s + s + (4/3)s
5 = s(3/4 + 1 + 4/3)
s = 60/37
side of square= 60/37
or. 1.621621621
or. = 1.63
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Because ABC is a 3-4-5 triangle, it is a right triangle.
Consequently, triangles ABC, PBS, SRC, and AQP are similar triangles. In each triangle, the longer leg to the shorter leg has a ratio of 4/3 (and the shorter leg to longer leg is a ratio of 3/4).
Suppose the square has a side length equal to s.
Then QR = s. In triangle SRC, SR = s, so RC = (4/3)s.
In triangle AQP, PQ = s, so AQ = (3/4)s.
Thus we have:
AC = AQ + QR + RC
AC = (3/4)s + s + (4/3)s
5 = s(3/4 + 1 + 4/3)
s = 60/37
side of square= 60/37
or. 1.621621621
or. = 1.63