Question

51. The perimeter of a square-shaped field is 100 m. How many plots each of can be made in the field? 25m ^ 2 (1) Four (3) Ten (2) Twenty-five (4) Six hundred and twenty-five ​

Answer 1

✬ 625 plots each of can be made in the field.Option(4)✬

Step-by-step explanation:

Given: Perimeter of square shaped field is 100 m.

To find: How many plots each of can be made in the field.

Required Formula:

• Perimeter of square = 4 × side
• Area of square = (Side)²

Where,

• Perimeter = 100
• Side = a

Applying the values,

$\\ \longmapsto\sf{100 = 4 \times a} \\ \\ \longmapsto\sf{a = \frac{100}{4}} \\ \\ \longmapsto\underbrace{ \boxed{ \mathfrak{a = 25}}} \: \red{ \bigstar}$

• Therefore,The side of square is 25 m.

Then,Finding the area of square

$\\ \longmapsto \: \sf{ A= {(25)}^{2} } \\ \\ \longmapsto \: \sf{ A= 25 \times 25} \\ \\ \longmapsto \: \underbrace{ \boxed{\mathfrak{A = 625 \: {m}^{2}}}} \: \blue{ \bigstar}$

• Hence,625 plots each of can be made in the plot. option(4)

Answer 2

★ 25 plots can be constructed over the field.

Step-by-step explanation:

Analysis -

⠀⠀In the question, it has been stated that the perimeter of a square-shaped field is 100 m, and we've been asked to find the number of plots each of 25 m² that can be created inside the field. Three options has been given.

• (1) Four
• (2) Ten
• (3) Twenty five
• (4) Six hundred and twenty five

Solution -

⠀⠀Generally, while solving any mathematical problem, we used to check whether the units of quantities are alike. Likewise, in our question, the two units aren't same since one quantity denotes area whereas the another quantity denotes perimeter. So, first let's find the area of the field to calculate the number of plots that can be created.

⠀⠀⠀⠀⠀Area of the square field

As per the formula, to find the area, we need the measure of length of side of the square field, which can be found by equating the given measure in the formula of perimeter of square.

$\dashrightarrow{ \sf{Perimeter_{ \{\square \}} = 4 (Side) \: units}} \\ \\ \dashrightarrow{ \sf{100 = 4(Side)}} \\ \\ \dashrightarrow{ \sf{ \dfrac{ \cancel{100}}{ \cancel4} = Side }} \\ \\ \dashrightarrow{ \underline{ \underline{ \sf \pmb{25 \: m = Side}}}}$

The side of the square equals 25 m. Now, let's the use the formula of area of square and find the area of the field.

$\dashrightarrow{ \sf{Area_{ \{\square \}} = {(Side)}^{2} \: sq.units}} \\ \\ \dashrightarrow{ \sf{ Area_{ \{\square \}}= {(25)}^{2} }} \\ \\ \dashrightarrow{ \sf{ Area_{ \{\square \}} =25 \times 25 }} \\ \\ \dashrightarrow\underline{ \boxed{ \sf \pmb{ Area_{ \{\square \}}= 625 \: {m}^{2} }}}$

Precisely, we have found the area of the square-shaped field. Now, we have to find the number of plots that can be made inside the field. As per the analysis, the area of one plot equals 25 m².

⠀No. of. plots that can be constructed

Total area of the field = 625 m²

Area of a square plot = 25 m²

Hence, the number of square plots that can be constructed is:

$\dashrightarrow{ \sf{ \dfrac{625 \: \cancel{{m}^{2}} }{25 \: \cancel{{m}^{2}} } }} \\ \\ \dashrightarrow{ \sf{ \dfrac{625}{25} }} \\ \\ \dashrightarrow{ \sf{ \dfrac{25 \cancel{(25)}}{1 \cancel{(25)}} }} \\ \\ \dashrightarrow{ \sf{ \dfrac{25}{1} }} \\ \\ \dashrightarrow \underline{ \boxed{ \frak{ \pmb {\red{25}}}}}$

• The number of plots that can be constructed is 25. Hence, third option is correct.

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