Question

a rectangular reflection pond in a park is 16 feet long. The maintenace crew placed a string of flags 20 feet long across the pond diagonally. What is the width of the pond in feet? A 12 B.) 144 C.) 4 D.) 26​

Answer 1

A.) 12

Explanation:

Each triangle has the proportions of a 3-4-5 right triangle, multiplied by 4 ft. The short side is 3·4 ft = 12 ft.

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In case you haven't run across 3-4-5 right triangles, you can use the Pythagorean theorem to find w. That tells you ...

20² = w² + 16² . . . . . the square of the hypotenuse is the sum of the squares of the other two sides

400 -256 = w² . . . . . subtract 16²; next, take the square root

√144 = w = 12 . . . . . feet

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Comment on 3-4-5 right triangles

There are a few "Pythagorean triples" that show up in algebra problems a lot. One is 3-4-5. Others are 5-12-13 and 7-24-25. It can be useful to keep these sets of numbers handy. The 3-4-5 triangle is also interesting because this is the only Pythagorean triple that is also an arithmetic sequence.