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

Why or why not?

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.

Answered by DavidOrrell | 2024-06-10

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.

4²+7²=16+49=11+5+49=65 (not 8²)

7²+8²=49+64=43+6+64=113 (not 4²)

4²+8²=16+64=80 (not 7²)

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

Answered by Anonymous | 2024-06-10

The triangle with sides 4, 7, and 8 is not a right triangle because the sum of the squares of the two shorter sides (16 + 49 = 65) does not equal the square of the longest side (64). Since the Pythagorean theorem is not satisfied, it confirms that the triangle is not right-angled.
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Answered by DavidOrrell | 2024-10-30