Does anyone know how to construct a square with the same surface area of a triangle? How do you get the length of the sides of the square?

Question

Does anyone know how to construct a square with the same surface area of a triangle?  How do you get the length of the sides of the square?

hero · Answer

Suppose the area of a triangle is 144 square feet. 
Then a square with the same area will have a side length of 12 feet. 

To demonstrate this, we'll need the formulas for the area of both the triangle and the square: 

$$A_{\triangle} = \frac{bh}{2}$$$$A_{\square} = s^2$$

Notice that if we have a triangle where b = 16ft. and h = 18ft., then we can calculate the its area as 144 sq ft.

We already stated that if we have a square of side length 12ft., we can calculate its area as 144 sq ft. as well since 12 x 12 = 144. 

I hope that helps.

anonymous · Answer

Thank you.  The problem example was all letters, but it makes more sense using real math.  I suppose that means that s equals the square root of bh/2?  Thanks again!

hero · Answer

Just keep in mind that those are two separate formulas with the same area.