Question

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Answer 1

Answer:

Given: The side of a square = 60 m

And the length of rectangular field = 80 m

According to question,

Perimeter of rectangular field

= Perimeter of square field

= 4 side

Now Area of Square field

= 3600 m2

And Area of Rectangular field

= length breadth = 80 40

= 3200

Hence, area of square field is larger.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Analysis :-

$\: \: \: \: \:$ We're given with the side and the length of a square and a rectangular field. And we're asked to find out that which field has a larger area of particular shape and dimensions.

• Dimension of the square field : Side = 60 m.
• Dimension of the rectangular field : Length = 80 m.

Understanding The Concept :-

$\: \: \: \: \:$ This question is from the chapter "Mensuration" which is the branch of Mathematics that deals with the computation of lengths, areas, or volumes from given dimensions or angles of a solid.

$\: \: \: \: \:$ The geometric figures focused in this question are square and rectangle. Rectangle is a quadrilateral with four sided polygonal figure with four right angles. Also, the diagonal bisects each other.

$\begin{gathered}.\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\huge \boxed{ \sf{ \: \: \: \: \: \: }}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tiny\sf{A \: rectangle} \end{gathered}$

• Perimeter = 2(l + b)
• Area = l × b

A square is also a quadrilateral that has four equal sides and equal angles. It's diagonal bisects at 90°.

$\begin{gathered}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge \boxed{ \sf{ \:}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tiny\sf{A \: square}\end{gathered}$

• Perimeter = 4 × side
• Area = (side)²

Solution :-

$\: \: \: \: \:$ As per the analysis, we need to find out that which field has a larger area. How can we find it? We can find it by using the topic :- "Area of rectangle and Area of square".

To find the required answer, we've to find out the breadth of the rectangle first. And then, we will find out the area of both square and rectangular field. And then, we'll check that which field has the larger area. Let's do it !

Calculations :-

➜ Finding the breadth of the rectangle :

$\: \: \: \: \:$ Since, we know that the perimeter of both square and rectangular field is same. So, by using the formula of perimeter of square and rectangle we'll find out the length of the rectangle.

$\longmapsto {\tt{Perimeter\ of\ rectangle\ =\ Perimeter\ of\ square}} \\ \\ \sf \longmapsto {2(l\ +\ b)\ =\ 4 \times side} \\ \\ \sf \longmapsto {2(80\ +\ b)\ =\ 4 \times 60} \\ \\ \sf \longmapsto {160\ +\ 2b\ =\ 240} \\ \\ \sf \longmapsto {2b\ =\ 240\ -\ 160} \\ \\ \sf \longmapsto {2b\ =\ 80} \\ \\ \sf \longmapsto {b\ =\ \dfrac{\cancel{80}}{\cancel{2}}} \\ \\ {\underbrace{\boxed{\sf{\red{B\ =\ 40\ m.}}}}_{\tiny\blue {\sf{Breadth}}}}$

➜ Finding area of the square :

$\: \: \: \: \:$ This calculation can be carried out by substituting the measures in the formula of area of square.

$\longmapsto {\tt{Area\ of\ square\ =\ (side)^2}} \\ \\ \sf \longmapsto {(60)^2} \\ \\ \sf \longmapsto {60 \times 60} \\ \\ {\underbrace{\boxed{\sf{\pink{3600\ m^2.}}}}_{\tiny\blue {\sf{Area\ of\ square}}}}$

➜ Finding area of the rectangle :

$\: \: \: \: \:$ On substituting the measures of length and breadth in the formula of area of rectangle we get,

$\longmapsto {\tt{Area\ of\ rectangle\ =\ l \times b}} \\ \\ \sf \longmapsto {80 \times 40} \\ \\ {\underbrace{\boxed{\sf{\pink{3200\ m^2.}}}}_{\tiny\blue {\sf{Area\ of\ rectangle}}}}$

$\: \: \:$ On checking the area of both square and rectangular field we find that the area of square field is larger. Hence, square field has larger area.