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Sagot :
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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