Question

The lengths of the three sides of a triangle are 4, 7, and 8. is the triangle a right triangle?

Why or why not?

Answer 1

If it's a right angled triangle, we should be able to set up an a²+b²=c² equation using 4,7 and 8. If this isn't possible, then the triangle isn't a right angled triangle.

4²=16, 7²=49 and 8²=64.

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4²+7²=16+49=11+5+49=65 (not 8²)

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7²+8²=49+64=43+6+64=113 (not 4²)

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4²+8²=16+64=80 (not 7²)

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Using this information we can see that the triangle you have described is not a right angled triangle.

Answer 2

In a right-angled triangle, a^2 + b^2 = c^2 (Pythagoras' theorem), where c is the hypotenuse (longest side) and a and b are the other two. 4^2 + 7^2 = 16 + 49 = 65, and 8^2 = 64. These numbers are not equal so the triangle doesn't follow the theorem - therefore it is not right-angled.