The base of triangle is one-third as long as it’s height. If the area of the triangle is 6 square meters, how long is its base?

Answer 1

The AREA OF A TRIANGLE is one-half times the base times the height. In other words, A = (1/2) (B) (H).

We need to solve for B in the equation above.

Furthermore, we are told the area is 6 square meters.

So A=6.

6 = (1/2) (B) (H)

And, we are told the base is one-third as long as the height.

So, B = (H/3).

Substitute (H/3) for B in 6 = (1/2) (B) (H) from above.

6 = (1/2) (H/3) (H)

6 = (H/6) (H)

6 = H^2/6 (Six equals H squared divided by 6.)

36 = H^2 (Multiplying both sides by 6.)

6 = H (Taking the square root of both sides.)

The height, H, is 6 meters, but we are determining the BASE, B.

Since the BASE is one-third of the HEIGHT,

B = 1/3 of 6 = 2.

_{THE BASE IS 2 METERS.}

CHECKING:

A = (1/2) (BASE) (HEIGHT) = (1/2) (2) (6) = (1) (6) = 6 and A = 6.

Therefore, the BASE IS 2 METERS.