Question

The length of one of the legs of a right triangle is 7. The lengths of the other two sides are consecutive integers. Use the Pythagorean theorem to solve for the smaller of the two missing sides (the second leg).

Answer 1

Answer: 24

Explanation:

Write out problem using Pythagorean Theorem:
`7^2+x^2=(x+1)^2`

Simplify and expand right side:
`49+x^2=x^2 + 2x + 1`

Subtract
`x^2` from both sides:
`49 = 2x + 1`

Subtract 1 from both sides:
`48=2x`

Divide by 2 on both sides:
`24 = x`

`x = 24`