Question

The length and breadth of a rectangle are (a + 3b) units and (5a - b) units
respectively. The perimeter of this rectangle is equal to the perimeter of a square.
Find the area of a Square?

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• Length of a rectangle = a + 3b units

• Breadth of a rectangle = 5a - b units

We know,

$\red{\boxed{\sf{ Perimeter_{(rectangle)} = 2(Length + Breadth)}}}$

So, on substituting the values, we get

$\rm :\longmapsto\:Perimeter_{(rectangle)} = 2(a + 3b + 5a - b)$

$\rm :\longmapsto\:Perimeter_{(rectangle)} = 2(6a + 2b)$

$\rm :\longmapsto\:Perimeter_{(rectangle)} = 4(3a + b) \: units$

According to statement

$\rm :\longmapsto\:Perimeter_{(square)} = Perimeter_{(rectangle)}$

$\rm :\longmapsto\:Perimeter_{(square)} = 4(3a + b)$

Let assume that the side of the square be x units

We know,

$\red{\rm :\longmapsto\:\boxed{\tt{ Perimeter_{(square)} \: = \: 4 \times side \: }}}$

So,

$\rm :\longmapsto\:4 \times x = 4(3a + b)$

$\rm\implies \: x = 3a + b \: units$

We know,

$\red{\rm :\longmapsto\:\boxed{\tt{ Area_{(square)} = {(side)}^{2} }}}$

So,

$\rm\implies \:Area_{(square)} = {(3a + b)}^{2} \: square \: units$

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$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$

Answer 2

Solution :-

given that,

→ Length of rectangle = (a + 3b) units

→ Breadth of rectangle = (5a - b) units

So,

→ Perimeter of rectangle = 2(Length + Breadth)

→ Perimeter of rectangle = 2(a + 3b + 5a - b)

→ Perimeter of rectangle = 2(6a + 2b)

→ Perimeter of rectangle = 4(3a + b)

now, let us assume that side of square is equal to m unit .

then,

→ Perimeter of rectangle = Perimeter of square

→ 4(3a + b) = 4m

→ m = (3a + b)

therefore,

→ Area of square = (Side)²

→ Area of square = m²

→ Area of square = (3a + b)²

→ Area of square = (9a² + b² + 6ab) unit² (Ans.)

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