# How do you find the area of the triangle when 24ft tall and the hypotenuse is 26ft?

Oct 9, 2015

The area would be $120 f {t}^{2}$

#### Explanation:

Pythagorean Theorem says this for triangle side lengths:

${a}^{2} + {b}^{2} = {c}^{2}$
c being the hypotenuse and a/b being the leg lengths

Therefore, we can plug in 26 for c, 24 for a, and solve for b, which will be the base.

${24}^{2} + {b}^{2} = {26}^{2}$
$576 + {b}^{2} = 676$
${b}^{2} = 100$
$b = 10$

Now that we know the base length, and the height, we can use the area for a triangle:

$\frac{1}{2} b h = A$

Let's plug in the remaining variables and solve for the answer.

$\frac{1}{2} \left(10\right) \left(24\right) = A$
$\frac{240}{2} = A$
$120 = A$

Put your units on ($f {t}^{2}$) and you get the answer at $120 f {t}^{2}$
Hope this helped!