Question

13. The area of a square field is 625m2. A rectangle
whose length is 4 times its breaslth has its perimeter
equals to Square perimeter. Find the area of rectangle
​

Answer 1

Answer:

400m^2

Step-by-step explanation:

Area of square = 625m^2

side of square = √625m^2

                        = 25 m^2

perimeter of square = 4 × side

                                  = 4 × 25 = 100 m

perimeter of rectangle = 100 m

ATQ, breadth = 'x'

         length = 4x

perimeter of rectangle = 2(l+b)

                                      =  2( 4x + x)

                                      = 8x + 2x

                                      = 10x

100 = 10x

100/10 = x

10 = x

therefore Breadth = 10 m and length (4x) = 4×10 = 40 m

Area of rectangle = l×b = 40 × 10 = 400 m^2

THEREFORE THE AREA OF RECTANGLE IS 400m^2

               

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer is 400 m²

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$\huge\sf\blue{Given}$

✭ Area of square field = 625 m²

✭ A rectangle has its length 4 times it's breadth

✭ Perimeter of rectangle is equal to perimeter of square

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$\huge\sf\gray{To \:Find}$

◈ Area of rectangle?

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$\huge\sf\purple{Steps}$

Perimeter of a square is given by,

$\underline{\boxed{\sf Area_{square} = a^2}}$

Substituting the given values,

➝ $\sf a^2=625$

➝ $\sf a=\sqrt{625}$

➝ $\sf a=25 \ m$

Perimeter of square is given by,

$\underline{\boxed{\sf Perimeter_{square} = 4a}}$

Substituting the values,

➝ $\sf Perimeter = 4a$

➝ $\sf 4\times 25$

➝ $\sf \red{Perimeter_{square} = 100 \ m}$

So now let the length of rectangle be 4x & breadth be x

Perimeter of rectangle is given by,

$\underline{\boxed{Perimeter_{rectangle} = 2(l+b)}}$

Substituting the values,

➳ $\sf Perimeter = 2(4x+x)$

➳ $\sf 2(5x)$

➳ $\sf \green{Perimeter_{rectangle} = 10x}$

Equating perimeter of rectangle and square

➠ $\sf 10x=100$

➠ $\sf x=\dfrac{100}{10}$

➠ $\sf x=10$

☯ Length of rectangle = 4 × 10 = 40 m

☯ Breadth of rectangle = 10 m

Area of rectangle is given by,

$\underline{\boxed{\sf Area_{rectangle} = Length\times Breadth}}$

Substituting the values,

»» $\sf Area = lb$

»» $\sf 40\times 10$

»» $\sf \orange{Area \ of \ rectangle = 400 \ m^2}$

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