Math Destroyer Test 5 Question 8

[z_m_96]

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The question says "the hypotenuse of a right triangle is 10 inches and of the other sides is 6 inches. What is the area of the triangle in square inches?"

This might be a dumb question but when I am drawing out this triangle. How do you know that sides would be 10, 8, and 6. Can you assume if the hypotenuse is 10 on a right triangle its a 3,4,5 triangle? or do you have to know at least the length of two sides to make that assumption.

Thanks Zack

 

[DMikes]

You need two sides.

C^2 = a^2 + b^2

100 = 36 + b^2

b = 8

 

[Krentist_72]

You need two sides to know the third. Pythagorean Theorem (as above) or recognizing it's a 3-4-5 right triangle, as you stated.
I think what you're asking is if they only gave you the hypotenuse being 10, could you assume it's a 3-4-5 right triangle? No. Think about it: it could be pretty much anything, like consider if it was a 45-45-90 isosceles triangle where the two other sides are the same, and therefore could not be 3-4-5.
If you don't recognize a pattern, use the Pythagorean theorem to be safe.

 

[z_m_96]

thanks for the responses guys. So then when it says "other sides is 6 inches" why is it not a isosceles triangle? it says other sides. When i first did this problem I drew a triangle that was 10,6,6 and found the area. Is it a typo in the question?

 

[Roy Williams]

thanks for the responses guys. So then when it says "other sides is 6 inches" why is it not a isosceles triangle? it says other sides. When i first did this problem I drew a triangle that was 10,6,6 and found the area. Is it a typo in the question?

Triangles with a right angle in them (right triangles) follow the pythagorean theorem rule. So just use that as a guideline. I don't think a 10,6,6 triangle would have a 90 degree angle anywhere in it.

 

[Krentist_72]

Must be a typo because it should say either "the other side is 6" or "the other sides are 6".... grammatically what you're saying is incorrect. And yeah, a right triangle wouldnt be 6-6-10. The pattern for a isosceles right triangle is x-x-x*root2. So if the hypotenuse was 10, and it was an isosceles right triangle, then the other two sides would be 5*squareroot of 2.

 

[z_m_96]

oh ok good point guys thanks for all the help