Question

A rectangle is 16m by 9m. find a side of the square whose area equal the area of the rectangle. By how much does the perimeter of the rectangle exceed the perimeter of the square


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Answer 1

$\huge\mathbb{SOLUTION:-}$

Area of rectangle=Area of square

• Dimensions of rectangle
• = >16 m and 9m

Now the area if rectangle

$\boxed{\sf{Area\:of\: rectangle=l\times b}}$

$\sf\implies Area\:of\: rectangle=16\times 9\\ \\ \sf\implies Area=144m{}^{2}$

• Area of rectangle is 144 square metre .

• So the Area of square is also 144 square metre

• Now the side of square

$\boxed{\sf{Area\:of\: square= side{}^{2}}}$

$\sf\implies Area=side{}^{2}\\ \\ \sf\implies 144=side{}^{2}\\ \\ \sf\implies \sqrt{144}=side\\ \\ \sf\implies side=12m$

• Side of square is 12m

• Now the perimeter of square

$\boxed{\sf{Perimeter\:of\:square=4\times side}}$

$\sf Perimeter\:of\:square=4\times 12\\ \\ \sf\implies perimeter=48m$

• Now the perimeter of rectangle

$\boxed{\sf{Perimeter\:of\: rectangle=2(l+b)}}$

$\sf\implies Perimeter\:of\: rectangle=2(16+9)\\ \\ \sf\implies Perimeter=2\times 25\\ \\ \sf\implies Perimeter=50m$

• Perimeter of rectangle is 50m.

• which is greater than perimeter of square by 2 m

$\boxed{\sf{\purple{Perimeter\:of\:square\:exceed\:by\:2m}}}$

Answer 2

Answer:

$\bf\green{Side\:of\:square=12\:m}$

$\bf\purple{Perimeter\:exceeds\:by\:2\:m}$

________________________

Given that,

• Dimensions of rectangle=16 m× 9m
• Area of rectangle=Area of square

Now,

${\boxed{\bold{Area\:of\:rectangle=Length\times Breadth}}}$

$\rightarrow\tt Area = (16 \times 9)\:{m}^{2} \\ \rightarrow\tt Area = 144 \:{m}^{2}$

${\boxed{\bold{Area\:of\:square={(Side)}^{2}}}}$

As per the question now,

$\rightarrow\tt {(Side)}^{2} = 144 \\ \rightarrow\tt Side =\sqrt{144}\:m \\ \rightarrow\tt Side = 12\:m$

$\therefore\bold{\underline{Side\:of\:square=12\:m}}$

________________________

${\boxed{\bold{Perimeter\:of\:rectangle=2(Length+Breadth)}}}$

$\tt Perimeter = 2(16+9)\:m \\ \rightarrow\tt Perimeter = (2 \times 25)\:m \\ \rightarrow\tt Perimeter = 50 \:m$

${\boxed{\bold{Perimeter\:of\:square=4\times side}}}$

$\rightarrow\tt Perimeter\:of\:square=(4 \times 12)\:m \\ \rightarrow\tt Perimeter = 48 \:m$

$\rightarrow\tt Perimeter\:exceeds\:by=(50-48)\:m \\ \rightarrow\tt Perimeter\:exceeds\:by=2\:m$

$\therefore\bold{\underline{Perimeter\:exceeds\:by=2\:m}}$