Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each hypotenuse length with the leg lengths that will create a right triangle.

Question

asked Jun 11, 2023 40.2k views

2 Answers

Wayland Smith · Answer 1 · 2023-06-15T11:31:15+0000

Answer:

see attached

Explanation:

The Pythagorean theorem can be used to find the hypotenuse associated with each pair of legs. That tells you ...

c² = a² +b² . . . . . legs a, b; hypotenuse c

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For the purpose of this problem, it is convenient to consider a slightly different form of the equation.

For legs √a and √b, the hypotenuse √c is given by ...

(√c)² = (√a)² +(√b)²

c = a +b

That is ...

legs √a, √b ⇒ hypotenuse √(a+b)

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Since the legs are (mostly) given in terms of square roots, the value under the radical for the hypotenuse is simply the sum of those:

legs: √1, √2 ⇒ hypotenuse √(1+2) = √3

legs: √2, √3 ⇒ hypotenuse √(2+3) = √5

legs: √5, √3 ⇒ hypotenuse √(5+3) = √8

legs: √5, √1 ⇒ hypotenuse √(5+1) = √6

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Additional comment

You may not see the leg lengths given as square roots very often. This is a rather unusual set of problems for hypotenuse length.