Question

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?

Answer 1

$<b>Heya mate. (^_-). Solution below.$
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$<u>Your Question - </u>$

A soccer field is a rectangle 90 m wide and 120 m long. The coach asks the players to run from one corner to the other corner diagonally. What is the distance covered by them?

$<u>Solution -</u>$

Length of the rectangular soccer field =
120 m.

Breadth of the rectangular soccer field =
90 m.

Now, we know that all the angles in a rectangle are at right angles, i.e., they all are 90°
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So, let's consider a situation in which -

AB (length) = 120 m

BC (breadth) = 90 m

Angle B = 90°

That makes a right angled triangle ABC, with AC as the hypotenuse (side opposite to the 90° angle)
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Now, the players run from A to C, so we have to find the length of diagonal AC.

Then, by Pythagoras Theorem

(Diagonal)² = (length)² + (breadth)²

=> diagonal² = (120)² + (90)²

= (120×120) + (90×90)

= 14400 + 8100

= 22500

=> diagonal² = 22500 m

=> diagonal = √22500

= √(150×150)

= 150

Hence, the length of diagonal AC = 150 cm.

$<marquee>Therefore, the players covered a distance of 150m.</marquee>$

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Thank you.. ;-)