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​

Given:

Area of a rectangle is [tex]600 \text{cm}^2[/tex].

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 = [tex]\dfrac{2}{3}x[/tex] cm

Area of a rectangle is

[tex]Area=Length \times Breadth[/tex]

[tex]600=x \times \dfrac{2}{3}x[/tex]

[tex]600=\dfrac{2}{3}x^2[/tex]

Multiply both sides by 3.

[tex]1800=2x^2[/tex]

Divide both sides by 2.

[tex]900=x^2[/tex]

Taking square root on both sides.

[tex]\pm \sqrt{900}=x[/tex]

[tex]\pm 30=x[/tex]

Length cannot be negative. So, x=30.

Now,

Length = [tex]30\text{ cm}[/tex]

Breadth = [tex]\dfrac{2}{3}\times 30\text{ cm}[/tex]

             = [tex]2\times 10\text{ cm}[/tex]

             = [tex]20\text{ cm}[/tex]

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

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