Question

Can the sides of a right triangle have lengths 7,9 and the square Root of 155

Answer 1

No

Explanation:

In order for a triangle to be a right angle, the sum of the squares of the two legs (a and b) must be equal the square of the longest side, known as the hypotenuse (c):

`a^2+b^2=c^2`

The square root of 155 is the longest side as it is approximately 12.45. Thus, if the triangle is a right triangle, the square root of 155 must be the hypotenuse.

We can now check to see whether the sum of the squares of 7 and 9 equal the square of the square root of 155:

`7^2+9^2=(√(155))^2\\ 49+81=155\\130=155`

The equation is not true since 130 is less than and not equal to 155. Therefore, a triangle with side lengths 7, 9, and the square root of 155 cannot be a right triangle.