A dog runs 100 yards from one corner of a rectangular park to the opposite corner. If the length of the park is 28 yards, what i

Question

pickupchik [31]

3 years ago

10

A dog runs 100 yards from one corner of a rectangular park to the opposite corner. If the length of the park is 28 yards, what i

s the width?

Mathematics

1 answer:

kap26 [50] · Answer 1 · 2022-03-13T05:46:20+03:00

9514 1404 393

Answer:

96 yards

Step-by-step explanation:

The diagonal through the park cuts the rectangle into two right triangles. The Pythagorean theorem tells you the relationship between the sides of a right triangle and its hypotenuse: the sum of the squares of the sides is equal to the square of the hypotenuse.

The diagonal is the hypotenuse, so we have ...

100² = 28² + w²

w = √(10000 -784) = 96

The width of the park is 96 yards.

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<em>Additional comment</em>

The integer side lengths of a right triangle form what is called a "Pythagorean triple." One of the most often seen of these is (3, 4, 5). Other commonly seen Pythagorean triples are (5, 12, 13), (7, 24, 25), (8, 15, 17).

You may notice that the numbers here are those of the (7, 24, 25) Pythagorean triple, multiplied by 4. If you recognize the given lengths as having the ratio 28:100 = 7:25, you have the clue you need to determine the answer simply from your knowledge of Pythagorean triples.