Tina would need a minimum of
The two triangles are
Then, by the properties of similar triangles:
Perimeter of #DFG = 15+18+21 = 54in.
This is the correct answer and a correct method for the solution.
There is also a method of solving the larger triangle with a formula to find the value of the common angle using the three given sides of the smaller triangle:
By the way that angle is
Then we can apply the same formula to the larger triangle:
When we see the triangles, we can say that the triangles are similar to each other. The corresponding sides are in multiples of their common sides.
We can say that,
Now we know the three sides of the triangle.We can find the area of the triangle using the Heron's formula
Let's apply the values to the formula
Split into prime factors
So, the minimum area of wood required is
Hope this helps...! :)