Answer:
[tex]\large\boxed{A_\triangle=25\sqrt{15}\ cm^2}[/tex]
Step-by-step explanation:
Look at the picture.
The formula of an area of a triangle:
[tex]A_\triangle=\dfrac{bh}{2}[/tex]
b - base
h - height
We need a length of a height.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have:
[tex]leg=5,\ leg=h,\ hypotenuse=20[/tex]
Substitute:
[tex]5^2+h^2=20^2[/tex]
[tex]25+h^2=400[/tex] subtract 25 from both sides
[tex]h^2=375\to h=\sqrt{375}\\\\h=\sqrt{(25)(15)}\\\\h=\sqrt{25}\cdot\sqrt{15}\\\\h=5\sqrt{15}\ cm[/tex]
Calculate the area:
[tex]A_\triangle=\dfrac{(10)(5\sqrt{15})}{2}=\dfrac{50\sqrt{15}}{2}=25\sqrt{15}\ cm^2[/tex]
