Question

The length of a rectangle is 24 cm and its diagonal is 30 cm. Find its breadth and area.

Answer 1

Let ABCD is a rectangle.

Length of rectangle = AB = CD = 24 cm

Breadth of rectangle = AD = BC = ?

Diagonal of rectangle (AC) = 30 cm

Apply Pythagoras theorem in ΔABC, we have:

(AC)² = (BC)² + (AB)²

(30)² = (BC)² + (24)²

(BC)² = (30)² – (24)²

(BC)² = (30 + 24)(30 – 24)

(BC)² = 56 × 4

BC = `sqrt(324)`

BC = 18 cm

Therefore, Area of rectangle = Length × Breadth

Area of rectangle = 24 cm × 18 cm = 432 cm²

Hence, the breadth of the rectangle is 18 cm and the area of the rectangle is 432 cm².