The base of a triangle is one half of its height. If the area of the triangle is 196 square millimeters. How do you find the height?

First write down the area of the triangle

A = 1/2 (B)(H)

Then plug in the numbers

196 = 1/2 (B)(H)
196 = 1/2 (B)(2B) --> which because the height is twice the base

Multiply both sides by 2

392 = (B)(2) (B)

Multiply B AND B
392 = 2(B^2)

Then divide both sides by 2.

196 = b^2

Finally, square root the number.

14mm = b

There we go, we got our base number which is 14. Now, we need to figure out the height which is twice the base.

So, 14 *2 is 28.

Our height is 28mm and base is 14mm.

Let h mm be the height of the triangle.
Then, the base of the triangle = h/2 mm

Area of the triangle in mm² :
(1/2) × h × (h/2) = 196
h²/4 = 196
h² = 784
h = √784
h = 28

The height of the triangle = 28 mm

Area of a triangle is 1/2 the product of the base (b) and the height (h); algebraically, A = (1/2)bh. Because the base is 1/2 the height, b = (1/2)h.

196 = (1/2)((1/2)h)(h)

196 = (1/4)h^2

784 = h^2

sqrt(784) = h

28 = h (discard -28).

The height of the triangle is 28 millimeters.

b = 1/2 h

(1/2) b * h = 196

(1/2) (1/2 h) * h = 196

(1/4) h^2 = 196

h^2 = 4 * 196

h = √(4 * 196)

h = 28 mm