Question

A man is running along the side of a square at a speed of 8 m/s .If he takes 1 minute 30 seconds to cover the perimeter once, find the area of the square.

Please help me to solve this mathematics question ​

Answer 1

Answer:

6400sqft

Step-by-step explanation:

Let parameter of square = A

And Let Side Of a Sqaure be X

So, Parameter of Sqaure = 4X

Let distance Covered by man be D

therefore distance covered by man Is eqaul to parameter of sqaure..

so ,

4X = D

Speed Of Man be S which is 8meter per sec

and time taken by man in sec is 90 seconds

so D = SxT

D= 8 x90 = 720

According to this

D = 4X =720

4X =720

X = 720/4 = 180

side of sqaure is = 180 = X

and Area Of That sqaure is side sqaure which is

6400sqaurefeet

Answer 2

$\displaystyle\large\underline{\sf\red{Given}}$

✭ A man is running around a square field with a speed of 8 m/s

✭ He takes 1 min 30 sec to complete one round

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ The area of a square

$\displaystyle\large\underline{\sf\gray{Solution}}$

So here we shall first convert the time to seconds,

➝ 1 min = 60 sec

➝ Total time = 60+30 = 90 sec

Then we'll find the distance using the formula for speed. Then b with that find the side v and finally calculate the area!!

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

So we know that,

$\displaystyle\underline{\boxed{\sf Speed = \dfrac{Distance}{Time}}}$

• Speed = 8 m/s
• Time = 90 sec

Substituting the values,

›› $\displaystyle\sf Speed = \dfrac{Distance}{Time}$

›› $\displaystyle\sf 8 = \dfrac{Distance}{90}$

›› $\displaystyle\sf 8\times 90 = Distance$

›› $\displaystyle\sf \purple{Distance = 720 \ m}$

Now then the side of the square will be given by,

$\displaystyle\sf \underline{\boxed{\sf Perimeter_{Square} = 4a}}$

• Perimeter = 720 m

Substituting the values,

➢ $\displaystyle\sf Perimeter = 4a$

➢ $\displaystyle\sf 720 = 4a$

➢ $\displaystyle\sf \dfrac{720}{4} = a$

➢ $\displaystyle\sf \orange{Side = 180 \ m}$

So then finally the area of a square is given by,

$\displaystyle\underline{\boxed{\sf Area_{Square} = Side^2}}$

• Side = 180 m

Substituting the values,

➳ $\displaystyle\sf Area = Side^2$

➳ $\displaystyle\sf Area = 180^2$

➳ $\displaystyle\sf \pink{Area = 32400 \ m^2}$

$\displaystyle\sf \therefore\:\underline{\sf Area \ of \ square \ is \ 32400m^2}$

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