69.1k views
4 votes
One leg of a right triangle has a length of 7m. The other sides have lengths that are consecutive integers. Find the lengths

User Admit
by
7.6k points

1 Answer

4 votes

Answer:

24 m, 25 m

Explanation:

You want the two sides of a right triangle that are consecutive integers when one side is 7 m.

Pythagorean theorem

Let the shorter side be represented by x. Then the longer side is x+1, and the Pythagorean theorem tells you ...

7² +x² = (x+1)²

49 +x² = x² +2x +1

48 = 2x . . . . . . subtract (x²+1)

24 = x

x+1 = 25

The other sides are 24 and 25 meters.

__

Additional comment

You know that 7 is not the hypotenuse, because a 3-4-5 right triangle is the only right triangle with consecutive integer leg lengths and a hypotenuse of 7 or less. (The next nearest right triangle with consecutive leg lengths is {20, 21, 29}, with a hypotenuse of 29.)

You may recognize the side lengths as the Pythagorean Triple {7, 24, 25}, one of the triples commonly seen in algebra and trig problems.

User Bijesh
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.