âPQRS is a rectangle. If PQ + QR = 7 and PR + QS = 10, then find the area of â PQRS.
PQ + QR = 7
PR + QS = 10
Since Diagonals of a rectangle are of equal length, so
PR = QS = 5
Let PQ be x, QR = 7 – x
Applying Pythagoras theorem :
x2 + (7 – x)2 = 52
⇒ 2x2 – 14x + 24 = 0
⇒ x2 – 7x + 12 = 0
⇒ x2 – 4x – 3x + 12 = 0
⇒ x(x – 4) – 3(x – 4) = 0
⇒ (x – 3)(x – 4) = 0
x = 3, 4
∴ The two sides are 3 and 4
Area of the Rectangle = (3 × 4) = 12 sq. units
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