a triangle has a base that is twice the length of its height. If the area of this triangle is 16 square inches, what is the height in inches

Question

I have this homework problem and I have tried to solve it on my own but I keep getting stuck as well as a couple of other problems that I am having ttrouble with. Please assist me

Answer 1

Well to answer this you've got to know what the area of a triangle is:

The formula for solving the area of a triangle is:

 

Area of a Triangle = 1 /2 Base * Height  which is;

 

A = 1/2 b * h

 

Now given A = 16 and b = 2h (2 times the height), we'll substitute the values into the formula

 

were A = 16 and b= 2h

 

16 = 1/2 (2h) * h

 

16 =  (2h / 2) * h

 

16 = ( h )* h .............[note 2h is divided by 2 which leaves us with just h]

 

16 = h²

 

and now to find h, we'll find the square roots of h² and 16 which give us;

 

√ 16 = √ h²

 

which gives;

 

4 = h

 

therefore, the height h = 4

 

 

 

Further more, if you are asked to find the length of the base, you'd just substitute the values of A and h into the formula.

 

That would be;

 

A = 1/2 b * h

 

A = 16, b = ? and h = 4

 

we'd have;

 

16 = 1/2 b * 4

 

16 = 4b / 2

 

16 = 2b

 

and the solve for b by dividing both sides by 2

 

16 / 2 = 2b / 2

 

8 = b

 

so the Base b = 8.

 

 

Hope this helps.

Answer 2

I echo Ebenezer O.'s solution, but would like to add that if you visualize the triangle, you might be able to see why the height is 4 inches.  Supposing the triangle was a right triangle (and even if not, but it's easier if you imagine it was right), you can visualize reshaping the triangle into a h-by-h square (h is the height).  Since the area of that square has to be 16 square inches, the side length, and therefore the height h, has to be 4.

 

It would be way easier to show if I could upload a picture. :( Hope this helps!  There are many ways to solve a problem, and it helps to solve it visually sometimes.