Question

the area of a rectangle is 600 cm2 and its breadth is two-third of its length find the length and breadth of the rectangle​

Answer 1

Given:

Area of a rectangle is
`600 \text{cm}^2`.

Breadth is two-third of its length.

To find:

The length and breadth of the rectangle​ .

Solution:

Let x cm be the length of the rectangle.

Then, Breadth or width of the rectangle =
`(2)/(3)x` cm

Area of a rectangle is

`Area=Length * Breadth`

`600=x * (2)/(3)x`

`600=(2)/(3)x^2`

Multiply both sides by 3.

`1800=2x^2`

Divide both sides by 2.

`900=x^2`

Taking square root on both sides.

`\pm √(900)=x`

`\pm 30=x`

Length cannot be negative. So, x=30.

Now,

Length =
`30\text{ cm}`

Breadth =
`(2)/(3)* 30\text{ cm}`

=
`2* 10\text{ cm}`

=
`20\text{ cm}`

Therefore, the length of the rectangle is 30 cm and the breadth is 20 cm.