The hypotenuse and a leg of a particular right triangle are \(\sqrt97\) inches and 4 inches, respectively. The area of this triangle is what common fraction of a square foot?
area of triangle = \(\frac12\) * base * height
We know the base is 4 inches. To find the height we can use the Pythagorean theorem.
42 + h2 = √[ 97 ]2
16 + h2 = 97
h2 = 81
h = 9
The height is 9 inches.
base = 4 inches = 4/12 feet = 1/3 feet
height = 9 inches = 9/12 feet = 3/4 feet
area of triangle = \(\frac12\cdot\frac13\cdot\frac34\ \) sq feet = \(\frac18\) sq feet