Question

Diagonal of a rectangle field is 17 metre and perimeter is 46 meter then area of the field will be.

Answer 1

Answer:

Hope it help. U

Bblegend

Answer 2

The area of the field will be 120 m².

Step-by-step explanation:

Let l and w are length and wight of the rectangle.

Diagonal of a rectangle:

$d=\sqrt{l^2+w^2}$

Diagonal of a rectangle field is 17 metre

$17=\sqrt{l^2+w^2}$

Taking square on both sides.

$17^2=l^2+w^2$

$289=l^2+w^2$               .... (1)

Area of a rectangle is

$A=l\times w$

Perimeter of a rectangle is

$P=2(l+b)$

Perimeter is 46 meter.

$46=2(l+b)$

Divide both sides by 2.

$23=(l+b)$

Taking square on both sides.

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

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

$529=(l^2+b^2)+2lb$            .... (2)

Form (1) and (2) we get

$529=289+2lb$

$529-289=2lb$

$240=2lb$

Divide both sides by 2.

$120=lb$

Therefore, the area of rectangle is 120 m².

#Learn more

The area of rectangle is 630 cm² and its lenght is 35 cm. ,find the perimeter of the rectangle?

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