Question

A rectangle is 16 m by 9 m. Find a side of the square whose area equals 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

Answer:

✦ Side of Square = 12 m

✦ 2 m

Step by Step Explanation:

Given :

• Length of Rectangle : 16 m
• Breadth of Rectangle : 9 m

$[/tex]</p><p><strong><u>T</u></strong><strong><u>o</u></strong><strong><u> </u></strong><strong><u>F</u></strong><strong><u>i</u></strong><strong><u>n</u></strong><strong><u>d</u></strong><strong><u> </u></strong><strong><u>:</u></strong></p><ul><li>side of the square whose area equals the area of the rectangle. </li></ul><p>[tex]$

Solution :

First we will find the Area of the Rectangle :

Area of Rectangle = l x b

✦ 16 x 9 = 144

Area of the rectangle is 144 m².

We know that area of a square =

side²

let the side be x.

✦ x² = 144

✦ x = √144

✦ x = 12

$[/tex] </p><p>Now we will find perimeter of Square and Rectangle :</p><p>Perimeter of Square = <strong> </strong><strong>s</strong><strong>i</strong><strong>d</strong><strong>e</strong><strong> </strong><strong>x</strong><strong> </strong><strong>4</strong></p><p>Perimeter of Rectangle = <strong> </strong><strong>2</strong><strong>(</strong><strong>l</strong><strong> </strong><strong>+</strong><strong> </strong><strong>b</strong><strong>)</strong></p><p>[tex]$

Pm of Square = 12 x 4 = 48

Pm of Rectangle = 2(16 + 9) = 50

Now we know the Perimeter of Square and rectangle.. Then,

50 m - 48 m = 2 m

$\rightarrowtail$ Hence if we exceed Perimeter of Square and rectangle we get 2 m.

Answer 2

As per the provided information in the given question, we have:

• Edges of rectangle are 16 m and 9 m.

We've been asked to find a side of the square whose area equals the area of the rectangle also we have to calculate difference in their perimeters.

“ Area of rectangle is length times the breadth. So, calculating the area of rectangle. ”

$\longrightarrow\quad\sf{{Area}_{(Rectangle)}=length\times breadth}$

Substituting values.

$\longrightarrow\quad\sf{{Area}_{(Rectangle)}=16\times 9}$

Performing multiplication.

$\longrightarrow\quad\bold{{Area}_{(Rectangle)}=144\: {cm}^{2}}$

According to the given condition.

$\longrightarrow\quad\sf{{Area}_{(Square)}={Area}_{(Rectangle)}}$

"Area of square is square of its side."

$\longrightarrow\quad\sf{{(Side)}^{2}={Area}_{(Rectangle)}}$

As, we have calculated the area of rectangle. So,

$\longrightarrow\quad\sf{{(Side)}^{2}=144}$

Transposing root from LHS to RHS.

$\longrightarrow\quad\sf{Side=\sqrt{144}}$

$\longrightarrow\quad\bold{Side=12\: m}$

– Now, we have to calculate the difference between the perimeter of Rectangle and that of square. Fo finding so, firstly we need to calculate the perimeter of square and perimeter of rectangle.

$\longrightarrow\quad\sf{{Perimeter}_{(Square)}=4\times Side}$

Here, the side of the square is 12 m. So,

$\longrightarrow\quad\sf{{Perimeter}_{(Square)}=4\times 12}$

Performing multiplication.

$\longrightarrow\quad\bold{{Perimeter}_{(Square)}=48\: m}$

Now,

$\longrightarrow\quad\sf{{Perimeter}_{(Rectangle)}=2(l+b)}$

Substituting values.

$\longrightarrow\quad\sf{{Perimeter}_{(Rectangle)}=2(16+9)}$

Performing addition.

$\longrightarrow\quad\sf{{Perimeter}_{(Rectangle)}=2(25)}$

Performing multiplication.

$\longrightarrow\quad\bold{{Perimeter}_{(Rectangle)}=50\: m}$

Now, finding their difference. $\\\longrightarrow\quad\sf{{Perimeter}_{(Rectangle)}-{Perimeter}_{(Square)}=50-48}$

Performing subtraction. $\\\longrightarrow\quad\bold{{Perimeter}_{(Rectangle)}-{Perimeter}_{(Square)}=2\: m}$

❝ By 2 meters the perimeter of the rectangle exceed the perimeter of the square. ❞