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 x AB

∴ 192 = I6 × AB 

∴ AB = 192/16

= 12cm 

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

∴ AC² = AB² + BC² [Pythagoras theorem] 

= 122 + 162 

= 144 + 2

=400 

∴ AC = √400 [Taking square root of both sides] 

= 20cm 

∴ The diagonal of the rectangle is 20 cm.