The longer leg of a right triangle is three times as long as the shorter leg. The hypotenuse is sqrt(5) What is the area of this triangle?
+33 We know that shortleg^2 + longleg^2 = \(\sqrt{5}^2\) or 5
If the shorter leg is x then the longer leg would be 3x
Therefore we have:
\(x^2 + 9x^2 = 5\)
simplify it to
\(10x^2 = 5\)
divide 4 each side
\(x^2 = \frac{5}{10}\)
square root both side
\(x = \sqrt{\frac{5}{10}}\)
So the shorter leg is \(\sqrt{\frac{5}{10}}\) and the longer leg is \(3 \sqrt{\frac{5}{10}}\)
Now we need to find the area
Multiply them:
\(3\sqrt{\frac{5}{10}}\cdot \sqrt{\frac{5}{10}} = 3 \cdot \frac{5}{10} = \frac{15}{10} = \frac{3}{2}\)
And don't forget we also have to divide by 2
\(\frac{3}{2} \div 2 = \frac{3}{4}\)
