Question

Select the correct answer from each drop-down menu.Phyllis bought 21 feet of wood to frame a window. If she makes a triangular window, what is the greatest area the window can have?For a given perimeter, the triangle with the largest perimeter isv triangle. Using this type of triangle, the sides wouldmeasureSo, the greatest area the window could be is aboutsquare feet

Answer 1

Equilateral Triangles

An equilateral triangle has all of its three sides of the same measure. Suppose the side length of an equilateral triangle is L.

The perimeter of such a triangle is:

P = 3L

Phyllis bought 21 feet of wood to frame a triangular window. This corresponds to the perimeter of the triangle, so we can calculate the side length:

L = P/3

L = 21 feet / 3

L = 7 feet.

Now we know the length of the side of the triangle, we calculate the area by using the formula:

`A=\frac{\sqrt[]{3}}{4}L^2`

Substituting L = 7 feet:

`\begin{gathered} A=\frac{\sqrt[]{3}}{4}(7ft)^2 \\ A=\frac{\sqrt[]{3}}{4}49ft^2 \\ \text{Calculating:} \\ A\approx21.22ft^2 \end{gathered}`