Finding the base and height of a triangle by the area

Question

The area of a triangle is 64 square centimeters. If both the base and height are doubled, what is the new area?



Answer 1

area of triangle = 1/2 * base * height

A = 1/2bh

These are all the relationships for the first triangle

64 = 1/2bh 128 = bh 128/b = h 128/h = b

For the second triangle, let y be it's area

y = 1/2(2b)(2h)

Plug in b or h or bh from the first triangle and solve for y.

Answer 2

Let "B" represent the length of the base of the triangle, and "H" represent the length of the height of the triangle. For the given triangle with an area of 64 square centimeters:

A = (1/2)BH = 64

If both the base and height lengths are doubled, this would result in lengths of 2B and 2H. Therefore:

A = (1/2)(2B)(2H) = (1/2)(BH)(4). Substituting 64 for (1/2)(BH):

A = (64)(4) = 256. Therefore, the new area of the triangle is 256 square centimeters.