Rectangle PQRS has PQ = 10 cm and QR = 12 cm. T is the midpoint of RS. Find the perimeter of triangle PQT.
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Worked Solution
Step 1: Set up the rectangle. P = top-left, Q = top-right, R = bottom-right, S = bottom-left.
PQ = 10 cm (top), QR = 12 cm (right).
Step 2: Find T, the midpoint of RS.
RS = PQ = 10 cm (opposite sides of rectangle are equal).
T is the midpoint, so RT = ST = 5 cm.
Step 3: Find QT using Pythagoras.
In right triangle QRT: QR = 12 cm (vertical), RT = 5 cm (horizontal).
QT = sqrt(12^2 + 5^2) = sqrt(144 + 25) = sqrt(169) = 13 cm.
Step 4: Find PT using Pythagoras.
In right triangle PST: PS = 12 cm (vertical), ST = 5 cm (horizontal).
PT = sqrt(12^2 + 5^2) = sqrt(169) = 13 cm.
Step 5: Perimeter of triangle PQT.
PQ + QT + PT = 10 + 13 + 13 = 36 cm.
Correct answer: 36 cm
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