Answer:
sides = 3.5 feet
area = 6.84 [tex]ft^{2}[/tex]
Explanation:
From the information provided in the question, this is a fairly simple algebraic equation. We are asked to solve for the length of the sides (s) which are all equal in length since this is an equilateral triangle and are given the value of p which is 126 inches. Now we simply plug-in this value for p and solve for s.
126 = 3s ... divide both sides by 3
42 = s
Since these are inches we can divide this value by 12 (12 inches = 1 foot) in order to find the length of s in feet.
42 / 12 = 3.5 feet
Now, we are also asked to find the area of the triangle which the equation for this is
[tex]A = \frac{1}{2} * base * height[/tex]
The base is 3.5 feet but in order to find the height we need to use pythagoreom theorem on half of the triangle which would be the following
[tex]h^{2} = a^{2} +b^{2}[/tex]
[tex]h^{2} = 3.5^{2} +(3.5/2)^{2}[/tex]
[tex]x^{2} = 12.25 + 1.75^{2}[/tex]
[tex]h^{2} = 15.3125[/tex] ... square root both sides
[tex]h = 3.91 ft[/tex]
Now we simply plug this into the area formula to calculate the area
[tex]A = \frac{1}{2} * base * height[/tex]
[tex]A = \frac{1}{2} * 3.5 * 3.91[/tex]
[tex]A = 6.84 ft^{2}[/tex]
