77 and 18+x are to sides of a right triangle

Find X.

1 answer

To find x in a right triangle, we can use the Pythagorean Theorem:

a^2 + b^2 = c^2

Where a and b are the two shorter sides of the triangle (in this case 77 and 18) and c is the hypotenuse (the side we are trying to find, x).

(77)^2 + (18 + x)^2 = x^2

Simplify the equation:

5929 + 324 + 36x + x^2 = x^2

Combine like terms:

6253 + 36x = x^2

Rearrange the equation to set it equal to zero:

x^2 - 36x - 6253 = 0

Now, we can solve for x by factoring or using the quadratic formula:

x = (36 ± √(36^2 + 4*1*6253)) / 2
x = (36 ± √(1296 + 25012)) / 2
x = (36 ± √26308) / 2
x = (36 ± 162.2) / 2

x = (36 + 162.2) / 2 ≈ 99.1
or
x = (36 - 162.2) / 2 ≈ -63.1

Since x represents a side length, it cannot be negative. So, x is approximately 99.1.