Question

The length of rectangular plot is thrice its breadth. If the area of the plot is 6075m²,what is its length?

Answer 1

Given:-

The area of the rectangular plot = 6075 m²

To be found

The length of the rectangular plot

According to the question,

The length of the rectangular plot is trice of its breadth

Let

breadth(b) = x m

length(l) = 3x m

Area of the rectangular plot = lb unit sq.

[∴In which l is the length and b is the breadth of the rectangular plot ]

⇒ 6075 = lb

⇒ 6075 = 3x*x

⇒ 6075 = 3x²

⇒ 6075 ÷ 3 = x²

⇒ 2025 = x²

⇒ $\bf \sqrt{2025}$ = x

⇒ 45 = x

Therefore

breadth = x = 45 m

and

length = 3x = 3*45 = 135 m

Answer 2

★ $\textsf{\large{Answer :}}$

$\textsf{Length = 135m}$

$\textsf{Breadth = 45m }$

★ $\textsf{\large{Explaination :}}$

★ $\textsf{\large{Given :-}}$

$\textsf{Area of the plot = 6075 sq.m}$

★ $\textsf{\large{To find :-}}$

$\textsf{Length and Breadth of the plot}$

★ $\textsf{\large{Solution :-}}$

$\texttt{Consider the Breadth as x}$

$\texttt{Consider the Length as 3x}$

$\mathbf{Area \: of \: Rectangle = L \times B}$

$\mathbf{= > 6075 = l \: \times \: b}$

$\mathbf{ = > 6075 = 3x \times x}$

$\mathbf{=> 6075 = {3x}^{2} }$

$\mathbf{ => {3x}^{2} = 6075 }$

$\mathbf{ => {x}^{2} = 6075 \div 3 }$

$\mathbf{ => {x}^{2} = 2025 }$

$\mathbf{=> x = \sqrt{2025} }$

$\begin{array}{r|l}5 & 2025\\\cline{1-2} 5& 405 \\\cline{1-2} 3 & 81\\ \cline{1-2} 3& 27 \\\cline{1-2} 3 & 9\\ \cline{1-2}3&3\\ \cline{1-2} &1 \end{array}$

Prime Factors of 2025 = 3, 3, 3, 3, 5, 5

Make pairs of same numbers and take only one from them

1.⟩ 3 and 3 → 3
2.⟩ 3 and 3 → 3
3.⟩ 5 and 5 →5

So, : 9 × 9 × 5

Again only one 9 will come so,

Square root of 2025 = 9 × 5

$\mathbf{x\: = 45}$

$\large{\green{\boxed{\green{\boxed{\red{\textsf{breadth \: = 45m}}}}}}}$

$\texttt{Length = 3x}$

$\mathbf{ = > 45 \times 3}$

$\large{\green{\boxed{\green{\boxed{\red{\textsf{length \: = 135m}}}}}}}$

★ $\texttt{\large{Verification}}$

$\mathbf{6075 = 135 \times 45}$

$\mathbf{ = > 6075 = 6075}$

$\therefore$$\textsf{LHS = RHS}$

$\therefore$$\textsf{Length = 135m}$

$\therefore$$\textsf{Breadth = 45m }$