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 = $\dfrac{2}{3}x$ cm

Area of a rectangle is

$Area=Length \times Breadth$

$600=x \times \dfrac{2}{3}x$

$600=\dfrac{2}{3}x^2$

Multiply both sides by 3.

$1800=2x^2$

Divide both sides by 2.

$900=x^2$

Taking square root on both sides.

$\pm \sqrt{900}=x$

$\pm 30=x$

Length cannot be negative. So, x=30.

Now,

Length = $30\text{ cm}$

Breadth = $\dfrac{2}{3}\times 30\text{ cm}$

             = $2\times 10\text{ cm}$

             = $20\text{ cm}$

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