Question

Find the diagonal of a rectangle whose length is 16 cm and area is 192 sq. cm.

Answer 1

Let ABCD be the given rectangle.

BC = 16cm

Area of rectangle = length × breadth

Area of ABCD = BC × AB

∴ 192 = I6 × AB

∴ AB = \(\frac{192}{16}\)

= 12 cm

Now, in ∆ABC, ∠B = 90° [Angle of a rectangle] 

∴ AC² = AB² + BC² [Pythagoras theorem] 

= 122 + 162 

= 144 + 256 

= 400

∴ AC = \(\sqrt{400}\) [Taking square root of both sides]

= 20cm 

∴ The diagonal of the rectangle is 20 cm.