Question

The area of a rectangle is 432 m and its breadth is one-third of its length.Find its breath and length

Answer 1

Given:-

Area = 432 m

Breadth = ${\frac{1}{3}}$ of Length

Assumption:-

Let Length = x metre

So,

Breadth = ${\frac{1}{3}}$ × x

= ${\frac{x}{3}}$ metre

Solution:-

As we know,

$\boxed{\sf{\green{A = l\times b}}}$

As we know area = 432 m

So,

432 = x × ${\frac{x}{3}}$

⟹ 432 = ${\frac{x^{2}}{3}}$

⟹ 432 × 3 = x²

⟹ 1296 = x²

⟹ $\sqrt{1296}$ = x

⟹ 36 = x

As, we know that the value of x = 36

So,

Length = x = 36 m

Breadth = ${\frac{x}{3}}$

= ${\frac{36}{3}}$

= 12 m

Required Answer:-

Breadth of the rectangle = 12 m

Length of the rectangle = 36 m

Answer 2

Given: The Length of a rectangle is three times of it's Breadth. & the area of the rectangle is 432 cm².

Need to find: The Perimeter?

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❍ Let's say, that the Breadth of plot be x m. Then, Length of the plot would be 3x m.

$:\implies\sf\quad Area_{\:(rectangle)} = Length \times Breadth$

$:\implies\sf\quad 432 = 3x \times x$

$:\implies\sf\quad x^2 = \cancel\dfrac{432}{3}$

$:\implies\sf\quad x^2 = 144$

$:\implies\sf\quad x = \sqrt{144}$

$:\implies\sf\quad x = 12$

Therefore, Length & Breadth are 36 cm and 12 cm.

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• P E R I M E T E R :

$:\implies\sf\quad Perimeter_{\;(rectangle)} = 2(Length + Breadth)$

$:\implies\sf\quad Perimeter = 2(12 + 36)$

$:\implies\sf\quad Perimeter = 2 \times 48$

$:\implies\sf\quad Perimeter = 96$

Hence, the Perimeter of rectangle is 96 cm.