triangle question

[xJoSephhhhh]

It won't let me past the picture but there is an image of a triangle. Two sides are larger than the third shortest side. The shortest side is 8 inch & one of the longer sides is 20 inch.

A company is making pennants or flags for a sports team. The team wants small versions for fans and large versions that will fly over the stadium. The dimensions of the small version are shown below.

1. The large version needs to be 12.5 feet across the base (the short side of the triangle). How long should it be?
   ft
2. How much material will be needed to make the large version of the flag? Round to the nearest tenth.
   sq. ft

Box 1: Enter your answer as a whole or decimal number. Examples: 3, -4, 5.5
Enter DNE for Does Not Exist, oo for Infinity
31.25
Box 2: Enter your answer as a whole or decimal number. Examples: 3, -4, 5.5
Enter DNE for Does Not Exist, oo for Infinity
195.3
The answers are displayed above but I am uncertain how they were obtained. If I were taught it in my math literacy course I would assume that you use the pythagorean theorum but we weren't. In this section we mostly used part over whole multiplied by one hundred. I don't see how that formula can be applied to this inquiry.

 

[MarkFL]

I am assuming the pennants are in the shape of an isosceles triangle. The ratio of the two longer sides to the shortest side is 5:2.

If we bisect the isosceles triangle into two congruent right triangles, what do we find is the altitude of the isosceles triangle, given the shortest side is the base?

 

[MarkFL]

Okay, after some trial and error to match the given answers, I found the pennant is in the shape of a right triangle, and the ratio of the legs is 5:2.

Hence, the length L of the large version in feet is:

\(\displaystyle L=\dfrac{25}{2}\cdot\dfrac{5}{2}=\dfrac{125}{4}=31.25\)

The area A in square feet is:

\(\displaystyle A=\dfrac{1}{2}bL=\dfrac{1}{2}\cdot\dfrac{25}{2} \cdot\dfrac{125}{4}=\dfrac{3125}{16}=195.3125\)