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31 votes
31 votes
Can a right triangle have the side lengths 4 mm, 13 mm, and 10 mm?

Justify your reasoning.

User Mariluz
by
2.9k points

2 Answers

16 votes
16 votes
Answer: No

Explanation:

Using Pythagoras Theorem,
Hypotenuse^2 = 1st Side^2 + 2nd Side^2

Consider the longest number, ie. 13mm as the Hypotenuse.

=> 13^2 = 4^2 + 10^2
=> 169 = 116
LHS is not Equal to RHS

Therefore, this denies the Pythagoras Theorem. Hence, a Right triangle cannot have these side lengths.
User Alejandro Caro
by
3.1k points
18 votes
18 votes

Answer:

No, because the given values do not produce a correct equation when plugged into the Pythagorean Theorem.

Explanation:

To solve this question, we can use the Pythagorean Theorem. (Also called Pythagoras Theorem)

The Pythagorean Theorem is true for ALL right triangles, meaning that if the side lengths don't work for it, the given triangle can not be a right triangle.

The theorem simply states that the sum of the squares of the two legs must add up to the square of the hypotenuse.

Note that the hypotenuse of a triangle is the side opposite to the right angle.

The Pythagorean Theorem can be easily written as the following expression:

a^2+b^2=c^2

This is where a and b are the legs and c is the hypotenuse.

We can plug our given values in to see if it's correct.

If it is a right triangle, the longest side will always be the hypotenuse, so we can safely set c as 13.

4^2+10^2=13^2

Simplify to see if it's true

16+100=169

116≠169

Therefore, a right triangle can not have these given side lengths.

Hope that helps, please let me know if you have any further questions!

User Cdiazal
by
2.8k points