Answer: If pqr ~ stu, then we know that the corresponding sides are proportional.
We have pq=25 and st=10, so we can find the ratio of corresponding sides as:
25 / 10 = 2.5
This means that each side of stu is 2.5 times smaller than the corresponding side of pqr.
The perimeter of pqr is 75, so we can find the length of the other sides by subtracting the length of pq from the perimeter and dividing by 2:
(pq + qr + rp)/2 = (25 + qr + rp)/2 = 75/2
25 + qr + rp = 75
qr + rp = 50
Since pqr ~ stu, we know that the ratio of perimeters is also 2.5. Therefore, the perimeter of stu is:
Perimeter of stu = 2.5 (st + tu + us)
We know st=10, so we can find the other sides as:
tu = qr / 2.5 = 50 / 2.5 = 20
us = rp / 2.5 = 50 / 2.5 = 20
Therefore, the perimeter of stu is:
Perimeter of stu = 2.5 (10 + 20 + 20) = 2.5 (50) = 125
So the perimeter of stu is 125.
Explanation: