# How do you find the area of a right triangle with the hypotenuse being 15 and one side being 12?

See explanation

#### Explanation:

Apply Pythagoras theorem to find the other side hence

${a}^{+} {b}^{2} = {c}^{2} \implies {a}^{2} = {15}^{2} - {12}^{2} = 81 \implies a = 9$

Now you know the base and the height of the triangle hence
the area of the triangle is

$A = \frac{1}{2} \cdot \left(b a s e\right) \cdot \left(h e i g h t\right) = \frac{1}{2} \cdot 9 \cdot 12 = 54$