Question

if the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm the area of the rectangle is

Answer 1

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Answer 2

Answer:

The area of the rectangle is 120 sq. cm.

Step-by-step explanation:

Given : If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm.

To find : The area of the rectangle is?

Solution :

Let the length of the rectangle be l

The breadth of the rectangle be b.

We have given,

Perimeter of the rectangle is 46.

Perimeter of the rectangle is given by,

$P=2(l+b)$

Substitute,

$46=2(l+b)$

$l+b=23$.....(1)

If the diagonal of a rectangle is 17 cm long.

The diagonal of the rectangle is given by

$D^2=l^2+b^2$

$17^2=l^2+b^2$

$289=l^2+b^2$ ......(2)

Now, Squaring the equation (1)

$(l+b)^2=(23)^2$

$l^2+b^2+2lb=529$

Substitute (2) in above equation,

$289+2lb=529$

$2lb=529-289$

$2lb=240$

$lb=120$

We know, multiple of length and breath is area of the rectangle.

Therefore, The area of the rectangle is 120 sq. cm.