Triangle formula to find base and height

Question

Hello, I am working with my 6th grade son and we have been doing Triangle formulas. He has gotten a lot better at the previous lessons but now we have to find the base and height of a triangle with only the area given. I have searched and haven't found much help. Here is the problem and need it worked out with the formula.

A triangle has an area of 7 square feet. What could be the length of the base and the height?

Answer 1

The only restrictions on each of the base and height are that they be a number of feet > 0 (the number doesn't have to be an integer; for example, the base could be .00000001 ft.

However, the key is that, one the height or base is specified, the other can be uniquely determined.

That is because the formula for the area of a triangle is 1/2 bh

Thus, if 1/2 bh =7 sq. ft., bh = 14 sq. ft.

Thus, given that the base is b ft., the height h in ft. will be 14/b

There would be the same formula for the base given the height; b = 14/h

Now, if the height and base had to be an integer number of feet, you could have (b, h) = (1, 14), (2, 7), (7, 2), or (14, 1)

Answer 2

Read the triangle as equilateral and not just triangle

Otherwise you do not get the answer

Area = 1/2 ( base ) ( height ) Let base = a , So height = (√3/2)a

7 = 1/2 a* (√3/2)a

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