Question

a rectangular field measuring 20m by 15m is divided in two identical square plot of a land find the largest possible length of a side of each square plot of a land ​

Answer 1

Answer :-

$\: \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Area of Square and Area of Rectangle has been used. According to this, its given that the rectangular field has been divided into two equal square plots. Then, the sum of area of two equal square plots will be equal to the area of whole rectangular field. Using this concept, let's do it..!!

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★ Formula Used :-

$\qquad \large{\boxed{\boxed{\tt{Area \: of \: Rectangle \: = \: Length(L) \: \times \: Breadth(B) }}}}$

$\: \qquad \large{\boxed{\boxed{\tt{Area \: of \: Square \: = \: (Side)^{2}}}}}$

AreaofSquare=(Side)2

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★ Question :-

A rectangular field measuring 20m by 15m is divided in two identical square plot of a land. Find the largest possible length of a side of each square plot of a land .

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★ Solution :-

Given,

» Dimensions of Rectangular plot = 20 m × 15 m

» Number of identical squares in which the rectangular plot has been divided = 2

Its given that, the land has been divided into two identical squares. Then, the area of these squares will be equal. Also, since areas of these squares will be equal thus the side of these squares also must be equal. Then,

• Let the side of each square be 'x' m

Then,

• Area of each square = x × x = x² sq. m

Then according to the concept, we get

➺ x² + x² = 20 × 15

Since area of both squares is equal.

➺ 2x² = 300 sq. m

$\quad \qquad \large{\bf{\longmapsto \: \: x^{2} \: = \: \dfrac{300}{2} \: = \: 150 m²}}$

⟼x 2= 2300

=150m²

➺ x² = 150 m²

$\qquad \qquad \large{\bf{\longmapsto \: \: x \: = \: \sqrt{150 \: m} = 5\sqrt{6} \: m \: or \: 12.25 \: m}}$

⟼x= 150m

=5/6

mor12.25m

$\qquad \qquad \large{\boxed{\boxed{\sf{x \: = \: 5\sqrt{6} \: m \: = \: 12.25 \: m}}}}$

x=5/6

m=12.25m

• Hence, the length of each side of square = x

= 5√6 m = 12.25 m

$\begin{gathered}\\ \boxed{\boxed{\rm{Hence, \: the \: largest \: possible \: length \: of \: the \: side \: of \: each \: square \: plot \: is \: [tex]\boxed{\underline{\bf{5\sqrt{6} \: m \: = \: 12.25 \: m}}}}}}\end{gathered}$

Hence,the largestpossiblelengthofthesideofeachsquareplotis

5

6

m=12.25m

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$\: \: \underline{\underline{\rm{\Longrightarrow \: \: Confused? \: Don't \: worry \: let's \: verify \: it \: :-}}}$

For verification, we need to simply apply the values we got into the equation we formed. Then,

➣ x² + x² = 20 m × 15 m

➣ (5√6 m)² + (5√6 m)² = 300 m²

➣ (25 × 6 m²) + (25 × 6 m²) = 300 m²

➣ 150 m² + 150 m² = 300 m²

➣ 300 m² = 300 m²

Clearly, LHS = RHS. So our answer us correct because the condition satisfies.

Hence, Verified.

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$\: \: \: \huge{\boxed{\tt{\large{More \: to \: know \: :-}}}}$

• Area of Circle = πr²h

• Area of Parallelogram = Base × Height

• Area of Triangle = ½ × (Base × Height)

• Area of Rhombus = ½ × (Sum of Paralle sides × Distance Between Them)

• Perimeter of Square = 4 × Side

• Perimeter of Rectangle = 2(Length + Breadth)

• Perimeter of Circle = 2πr

* Note :- Here we get the value of largest possible side of each square to be 5√6 m or 12.25 m. Both are same values actually. For your comfort you can use any of them. Both are correct answers.

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Answer 2

Answer:

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