Find base and height of triangle from only its area?

Question

"An equilateral triangle has an area of 3 cm^2 determine the length of its base and its height to 2 decimal places"

Thats the question and I dont know how to do it.
I think you have to split it, create a right triangle then use the ratio
1:(sqrt)3:2 (because its a 30,60,90 triangle) but I cant get further than that. The answer in the back of the book is 8.32 and 7.21 cm

Help

Answer 1

Most answers above are in the right direction. Here is a simple step-wise solution. Area of any triangle is (1/2) base x height.In an equilateral triangle , base and height are inter-related.The perpendicular dropped from the apex bisects the base.Let the side of the equit triangle be x. What is its height?You now have a rt-angled triangle with base x/2 and hypotenuse x. ( Draw it on paper to follow the next steps) Apply Pythagorus theorem to caclulate the height. Height squared is x^2-(x/2)^2=3x^2/4
It is difficult to explain the steps in English , without symbols for root ,etc.

From the above you have ht h in terms of x

Area is (1/2) h x=3.Plug in value for h to get an eq for x^2. Solve for x. Go back to derived formula for h to get h
If you still have difficulty , feel free to send me an email

Answer 2

The area is .5*h*B. Since it is an equilateral triangle, the sides are also B in length If you look at half the triangle as divided by the altitude h, there are two right triangles, with hypotenuse B and base B/2. The height therefore is h = √[B^2 - (B/2)^2] = B√(.75). Therefore the area is A = .5*B*B√(.75). Solve for B

EDIT: Correction made: forgot to square the (1/2) to make (1/4).

BTW, the answer comes out h=2.28cm, B=2.63cm

Answer 3

The area is 30. Area = 1/2 base x height.

Answer 4

You're right about the 30-60-90 thing, since you'll get two of those when you chop the equilateral triangle in half. We need a variable in there like t. The height of the traingle is t*root(3), and the base is 2t (the ratio has t, which would be half of the base). The area of a triangle is base * height / 2, so....
area = (2t) * (t*root(3)) / 2 = 3 cm^2
After you know the value of t, you can go back and plug it into your equations for height = t*root(3) and width = 2t.

Answer 5

Those answers cannot be correct, because multiplying that base and height together gives over 56cm^2. But the area of a triangle is base*height/2, that gives about 28cm^2. That is far different from the 3cm^2 you started with as the area of the triangle.

Answer 6

I'm not selling the entire punch here, but the secret lies in the formula for getting the area of any triangle is always the same.

And if you split the current area of the triangle in 2, then you can work your way backwards.

HTH