Question

In the figure area of triangle ABD is 10cm and area of triangle ADC is 12cm²

a) Find BD:DC

Answer 1

Answer:

Same as always, what’s the area of a triangle?

Do like this

Step-by-step explanation:

1/2 base x height. Always. (Although you should learn how to prove Heron’s formula as well.)

Let’s take the base as BC. It’s still the base even when a line from the top A drops to outside it - just consider the extended line CB.

Work out the height using the given side AB and the given angle.

AB becomes the hypotenuse of a right triangle where the ‘opposite’ side is the height, a perpendicular dropped from A to the base-line.

Sine formula, anyone?

Okay, go ahead, you can do it on your own now.

So, why is the area 1/2 base x height?

(Even if the top A is shifted along a parallel to BC. Do you see that?)

Hint: make the triangle into a parallelogram by doubling it and flipping it over, joining it along a side.

Note that whatever the corner angles of the parallelogram, the area is the same = base x height. See how you can make the parallelogram into an oblong by chopping off a right triangle on the side & flipping it to the other side. You already know the area of an oblong. That’s twice the area of the triangle you started with.

Hope it helps