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What is the area of a rectangle whose length is 16cm and the length of the diagonal is 20cm?

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100

c m 2

114

c m 2

192

c m 2

196

c m 2

answer is C.

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Detailed Solution

We know that area of a rectangle is length

×

breadth.
Let us take a rectangle ABCD where the length of a rectangle is AB=16cm and the length of the diagonal that is AC=20cm.
Question Image

To find the area of the rectangle we will need to find the breadth of the rectangle.
So, we will use the Pythagoras theorem in triangle ABC since each angle of a rectangle is 90 degrees.
In triangle ABC,

A C 2 = B C 2 + A B 2

202 = B C 2 + 162

B C 2 = 400 − 256

B C 2 = 144

B C 2 = 122

B C = 12 c m

Now, we will be able to find the area of rectangle ABCD.
Area of rectangle

= A B × B C

= 16 c m × 12 c m

= 192 c m 2

Hence, option 3 is correct.

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