Question

Question

Find the percentage change in area when each sides exceed by 25%.​

Answer 1

$❤️ Solution❤️$

Given

• Each sides of a Square is increased by 25 %.

To Find

• Percentage change in its area.

Step by step explanation:

Let Each sides of a Square be x.

$\sf\footnotesize\implies Area \: of \: Square = (Side)²$

$\sf\footnotesize\implies Area \: of \: Square = (x)²$

• Now Sides increase by 25%

${\small \implies \bf{New}\sf ~Side ~of ~Square = Side × \: \bigg(\dfrac{100+Increase\%}{100} \bigg)}$

${\small \implies \bf{New}\sf ~Side ~of ~Square = x \: \bigg(\dfrac{100+25}{100} \bigg)}$

${\small \implies \bf{New}\sf ~Side ~of ~Square = \: \dfrac{125x}{100} }$

${\small \implies \bf{New}\sf ~Side ~of ~Square = \: \dfrac{5x}{4} }$

• New Area

${\small\sf \implies New \: Area \: of \: Square = \bigg(\dfrac{5x}{4} \bigg) ^{2} }$

${\small\sf \implies New \: Area \: of \: Square = \dfrac{25 {x}^{2} }{16} }$

• Increased Area

${\sf\implies Increase \: Area = New~ Area - Area }$

${\sf\implies Increase \: Area = ~ \dfrac{25 {x}^{2} }{16} - {x}^{2} }$

${\sf\implies Increase \: Area = ~ \dfrac{25 {x}^{2} - 9 {x}^{2} }{16} }$

${\sf\implies Increase \: Area = ~ \dfrac{9 {x}^{2} }{16} }$

• Now Increase Area percent

${\sf\implies Increase \: Area \% = \dfrac{Increase \: Area}{Area} × 100 }$

${\sf\implies Increase \: Area \% = \dfrac{ \frac{9 {x}^{2} }{16} }{ {x}^{2} } × 100 }$

${\sf\implies Increase \: Area \% = \dfrac{ 0.5625 {x}^{2} }{ {x}^{2} } × 100 }$

${\sf\implies Increase \: Area \% = 0.5625 × 100 }$

${\sf\implies Increase \: Area \% = 56.25 \% }$

• 56.25% percentage change in area when each sides exceed by 25%.

$\\\\\begin{gathered}\\\\\\\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \bigstar \: \underline{\bf{More \: Useful \: Formula}}\\ {\boxed{\begin{array}{cc}\dashrightarrow {\sf{Perimeter \: of \: rectangle = 2(l + b)}} \\\\ \dashrightarrow \sf{Area \: of \: rectangle = length \: \times breadth }\\ \\ \dashrightarrow \sf{Perimeter \: of \: square = 4 \times side } \\ \\ \dashrightarrow \sf{Area \: of \: square =(side) ^{2} } \\ \\ \dashrightarrow \sf{Area \: of \: parallelogram = base \times height} \\ \\ \dashrightarrow \sf{Area \: of \: trapezium = \frac{1}{2}×sum \: of \: parallel \: side \: \times \: height }\\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

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Explanation:

Let each side of the square be a. Then, area = .a2

New side =125a100=5a4. New area = (5a4)2 = (25a216)

Increase in area = 25a216−a2=9a216

Increase% = [9a216*1a2*100]% = 56.25%