Question

Find the area of a rectangle whose perimeter is 10 cm and diagonal is √15

Answer 1

The area of the rectangle is 5 sq cm.

• The perimeter of the rectangle is 10 cm.
• Length of the diagonal is √15 cm.
• Let the length and breadth of the rectangle be l and b respectively.

• Using Pythagoras theorem in rectangle ABCD,

AB² + AD² = BD²

l² + b² =(√15)²

l² + b² = 15     (Equation 1)

• Now,

2 (l+b) = 10

l + b = 5

• Squaring both sides we get,

l² +2lb + b² = 5²

15 + 2lb = 25               (From equation 1)

2lb = 10

lb = 5

• Now , area of rectangle is given by the product of length × breadth

Area = lb = 5 sq. cm

Answer 2

Answer:

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