The length of a rectangle is 16 cm and the length of its diagonal is 2

1.	The length of a rectangle is 16 cm and the length of its diagonal is 20 cm. The area of the rectangle is(a) 320 cm2 (b) 160 cm2 (c) 192 cm2 (d) 156 cm2
Answer» (c) 192 cm² Because, Let ABCD be the rectangular plot. Then, AB = 16 cm and AC = 20 cm BC =? According to Pythagoras theorem, From right angle triangle ABC, we have: = AC² = AB² + BC² = 20² = 16² + BC² = BC² = 20² – 16² = BC² = 400 – 256 = BC² = 144 = BC = √144 = BC = 12 cm Hence, the area of the rectangle plot = (l × b) Where, l = 16 cm, b = 12 cm Then, = (16 × 12) = 192 cm²

The length of a rectangle is 16 cm and the length of its diagonal is 20 cm. The area of the rectangle is(a) 320 cm2 (b) 160 cm2 (c) 192 cm2 (d) 156 cm2

Answer»

(c) 192 cm²

Because,

Let ABCD be the rectangular plot.

Then, AB = 16 cm and AC = 20 cm

BC =?

According to Pythagoras theorem,

From right angle triangle ABC, we have:

= AC² = AB² + BC²

= 20² = 16² + BC²

= BC² = 20² – 16²

= BC² = 400 – 256

= BC² = 144

= BC = √144

= BC = 12 cm

Hence, the area of the rectangle plot = (l × b)

Where, l = 16 cm, b = 12 cm

Then,

= (16 × 12)

= 192 cm²