Explanation:
We can use the information given about the perimeter of the triangle to set up an equation:
PQ + QR + PR = 75
Substituting the given expressions for each side, we get:
(4y + 2) + (y + 3) + (5y) = 75
Simplifying the left-hand side, we get:
10y + 5 = 75
Subtracting 5 from both sides, we get:
10y = 70
Dividing both sides by 10, we get:
y = 7
Now that we know the value of y, we can substitute it back into the expressions for each side of the triangle to find their lengths:
PQ = 4y + 2 = 4(7) + 2 = 30
QR = y + 3 = 7 + 3 = 10
PR = 5y = 5(7) = 35
Therefore, the lengths of the sides of the triangle are:
PQ = 30
QR = 10
PR = 35