Find the height of an isosceles trapezoid who's bases are 8 inches and 24 inches and the legs are 17 inches.
To find the height of an isosceles trapezoid, you can use the Pythagorean theorem. The height (h) can be calculated using the legs (a and b) of the trapezoid and the difference in lengths of the bases (c).
In this case, the legs (a and b) are given as 17 inches each. The difference in base lengths (c) is the absolute value of the difference between 8 inches and 24 inches, which is 16 inches.
Now, you can substitute the values for a, b, and c into the Pythagorean theorem formula, which is:
a^2 + h^2 = b^2
Using the given values:
17^2 + h^2 = 16^2
289 + h^2 = 256
To isolate h, subtract 289 from both sides:
h^2 = 256 - 289
h^2 = -33
Since the height value cannot be negative, it means that there is no real solution for the height of this isosceles trapezoid with the given measurements.