Question

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

Answer 1

Hello !!



Let ABCD is a rectangle.



Length of rectangle = AB = CD = 24 cm

Breadth of rectangle = AD = BC = ?

Let Diagonal (AC ) = 30 cm

By Pythagoras theorem , we have :

BC = ✓ ( AC)² - (AB)² = ✓(30)² - (24)²

=> ✓( 30 + 24 ) ( 30-24)

=> ✓54 × 6

=> ✓324

=> 18 cm

Breadth ( AD ) = BC = 18 cm

Therefore,

Area of rectangle = L × B




=> 24 × 18

=> 432 cm².

Answer 2

The Diagonal of the rectangle are divides its 2 right angled triangle , so we can use the Pythagorean theorem to solve this problem.
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GIVEN

Length of Rectangle = 24 cm

Diagonal of Rectangle = 30 cm
__________

=> [hyp]² = [lenght]² + [breadth]²

=> 30² = 24² + [breadth]²

=> [breadth]² = 900 - 576 = 324

=> Breadth = 18 cm
___________

NOW,

Area of Rectangle = Length × Breadth

= 24 × 18 = 432 cm²
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