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

Step-by-step explanation:

Answer

(c) 192cm

2

Because,

Let ABCD be the rectangular plot.

Then, AB=16cm and AC=20cm

BC=?

According to Pythagoras theorem,

From right angle triangle ABC, we have:

=AC

2

=AB

2

+BC

2

=20

2

=16

2

+BC

2

=BC

2

=20

2

−16

2

=BC

2

=400−256

=BC

2

=144

=BC=

144

=BC=12cm

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

Where, l=16cm,b=12cm

Then,

=(16×12)

=192cm

2