Question

A square and a rectangle have the same perimeter. Calculate the area of the rectangle if the side of the square is 60 cm and the length of the rectangle is 80 cm.

Note:
- Need full Explanation
- Don't Spam​

Answer 1

Given

• A square and a rectangle have the same perimeter.
• Side of the square is 60 cm.
• Length of the rectangle is 80 cm.

___________________________

To Find

• The area of the rectangle.

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Solution

With the measure of the side of the square given, let's find the perimeter of the square first.

Formula to Find Perimeter of Square → 4 × (Side)

Side → 60 cm

Perimeter of Given Square → 4 × 60

Perimeter of Given Square → 240 cm

∴ The perimeter of the given square is 240 cm

Now we have to find the value of the breadth of the given rectangle in order to be able to obtain the area. So using the perimeter of the square, let's find the breadth of the rectangle.

Formula to Find Area of Rectangle → 2 (Length + Breadth)

Length → 80 cm

Breadth → x cm

Perimeter of Square = Perimeter of Rectangle

240 cm = 240 cm

Let's solve the below equation step-by-step to find the value of the breadth.

2 (80 + x) = 240

Step 1: Simplify the equation.

⇒ 2 (80 + x) = 240

⇒ 2 (80) + 2 (x) = 240

⇒ 160 + 2x = 240

Step 2: Subtract 160 from both sides of the equation.

⇒ 2x + 160 - 160 = 240 - 160

⇒ 2x = 80

Step 3: Divide 2 from both sides of the equation.

⇒ 2x ÷ 2 = 80 ÷ 2

⇒ x = 40

∴ The breadth of the rectangle → 40 cm

According to the question, we'll have to find the area of the rectangle now.

Formula to Find The Area of Rectangle → Length × Breadth

Length → 80 cm

Breadth → 40 cm

Area of Given Rectangle → 80 × 40

Area of Given Rectangle → 3200 cm²

∴ The area of the given rectangle is 3200 cm²

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Answer 2

${\large{\pmb{\sf{\underline{RequirEd \; Solution...}}}}}$

${\pmb{\sf{\underline{Understanding \: the \: question...}}}}$

⋆ This question says that a square and a rectangle have the same perimeter. We have to calculate the area of the rectangle if the side of the square is 60 centimetres and the length of the rectangle is 80 centimetres. Let us solve this question!

${\pmb{\sf{\underline{Given \: that...}}}}$

⋆ Square and rectangle are given.

⋆ They have same perimeters.

⋆ The side of the square is 60 centimetres.

⋆ The length of the rectangle is 80 centimetres.

${\pmb{\sf{\underline{To \: calculate...}}}}$

⋆ The area of the rectangle

${\pmb{\sf{\underline{Solution...}}}}$

⋆ The area of the rectangle = 3200 cm²

${\pmb{\sf{\underline{Using \: concepts...}}}}$

⋆ Formula to find out the area of the rectangle.

⋆ Formula to find out the perimeter of the rectangle.

⋆ Formula to find out the perimeter of the square.

${\pmb{\sf{\underline{Using \: formulas..}}}}$

${\small{\underline{\boxed{\sf{\star \: Area \: of \: rectangle \: = Length \times Breadth}}}}}$

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

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

${\pmb{\sf{\underline{Full \; Solution...}}}}$

~ Firstly by using the formula to find out the perimeter of square let us find perimeter of the given square.

${\small{\underline{\boxed{\sf{Perimeter \: of \: square \: = 4 \times side}}}}} \\ \\ :\implies \sf Perimeter \: of \: square \: = 4 \times side \\ \\ :\implies \sf Perimeter \: of \: square \: = 4 \times 60 \\ \\ :\implies \sf Perimeter \: of \: square \: = 240 \: cm$

Henceforth, 240 centimetres is the perimeter of the square.

~ Now as it's given that square and a rectangle have the same perimeter. Now we have to use the formula to find out the perimeter of the rectangle to find the breadth of rectangle as length is already provided to us!

${\small{\underline{\boxed{\sf{Perimeter \: of \: rectangle \: = 2(l+b)}}}}} \\ \\ :\implies \sf Perimeter \: of \: rectangle \: = 2(l+b) \\ \\ :\implies \sf 240 \: = 2(80+b) \\ \\ :\implies \sf 240 \: = 160 + 2b \\ \\ :\implies \sf 240 - 160 \: = 2b \\ \\ :\implies \sf 80 \: = 2b \\ \\ :\implies \sf \dfrac{80}{2} \: = b \\ \\ :\implies \sf \cancel{\dfrac{80}{2}} \: = b \\ \\ :\implies \sf 40 \: = b \\ \\ :\implies \sf b \: = 40 \: cm$

Henceforth, we get breadth of the given rectangle as 40 centimetres.

~ Now let's find out the area of the rectangle by using the formula.

${\small{\underline{\boxed{\sf{Area \: of \: rectangle \: = Length \times Breadth}}}}} \\ \\ :\implies \sf Area \: of \: rectangle \: = Length \times Breadth \\ \\ :\implies \sf Area \: of \: rectangle \: = 80 \times 40 \\ \\ :\implies \sf Area \: of \: rectangle \: = 3200 cm^2$

Henceforth, area of rectangle is 3200 centimetres sq.

${\pmb{\sf{\underline{Figure...}}}}$

According to the question:

$\begin{gathered} \sf 80 \: cm \: \: \: \: \: \: \: \: \: \: \: \\ \begin{gathered}\begin{gathered}\boxed{\begin{array}{}\bf { \red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}\end{gathered}\end{gathered} \sf 40 \: cm \end{gathered}$

${\large{\pmb{\sf{\underline{Additional \; information...}}}}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Area \: of \: rectangle \: = \: Length \times Breadth}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Perimeter \: of \: rectangle \: = \: 2(length+breadth)}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Perimeter \: of \: square \: = \: 4 \times sides}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Area \: of \: square \: = \: Side \times Side}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Area \: of \: triangle \: = \: \dfrac{1}{2} \times breadth \times height}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Area \: of \: paralloelogram \: = \: Breadth \times Height}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Area \: of \: circle \: = \: \pi r^{2}}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Perimeter \: of \: triangle \: = \: (1st \: + \: 2nd \: + 3rd) \: side}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Perimeter \: of \: paralloelogram \: = \: 2(a+b)}}$