Question

The length of a rectangle is 16 cm and the length of its diagonal is 20 cm. Find the area of the rectangle​ ​

Answer 1

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The Length, breadth and Diagonal of a rectangle form a right-angled triangle with the length and breadth as the perpendicular sides and the diagonal as the hypotenuse.

∴ diagonal² = length² + breadth² (by the Pythagorean theorem)

∴ 20² = 16² + b²

⇒ 20² - 16² = b²

⇒144 = b²

∴ b = √144 cm = 12 cm

Area of rectangle = length × breadth

= (16 × 12)cm²

= 192 cm²

Answer 2

Answer:

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The Length, breadth and Diagonal of a rectangle form a right-angled triangle with the length and breadth as the perpendicular sides and the diagonal as the hypotenuse.

∴ diagonal² = length² + breadth² (by the Pythagorean theorem)

∴ 20² = 16² + b²

⇒ 20² - 16² = b²

⇒144 = b²

∴ b = √144 cm = 12 cm

Area of rectangle = length × breadth

= (16 × 12)cm²

= 192 cm²