Question

If the perimeter of an equilateral triangle is 30 ft, what is the area?

Answer 1

an equilateral triangle has 3 EQUAL sides
the perimeter is the sum of the lengths of all sides
so the 30 has to be divided equally into 3\[30\div3=10\]so each side is \(10ft\)

the equation to find the area of a triangle is \(A_{triangle}={1\over2}bh\)

find the height of the triangle by using the pythagorean theorem \(a^2+b^2=c^2\)
we know that the base \(a\) of the RIGHT triangle (formed by the line drawn down the middle) is 5 (half of 10 is 5) and the hypotenuse \(c\) is 10 so lets plug that in:\[5^2+b^2=10^2\]\[25+b^2=100\]\[b^2=75\]\[b=\sqrt{75}\]so now we know that the height of the triangle is \(\sqrt{75}\) now plug in these values into the area formula:\[A={1\over2}(10)(\sqrt{75})\]\[A=5\sqrt{75}\]
hope this helps! :)