Matt H. answered • 01/05/15
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Hi Ash,
I'm not sure we can answer the second part of the question (area of DCEB) without knowing how the two triangles are attached to one another,
BUT I think we can do the first part:
If area of ADE = 6 cm squared, that means the height of that triangle is 4 cm, because the area will be 1/2 of 3 * 4.
So if the height of that one is 4, the height of the other one will be 6.6666 repeating, because the similar sides of the 2 triangles are in a 3:5 ratio, so the heights will be as well.
So the area of ABC will be 1/2 * 5 * 6.6666, which will be ....approximately 16.667.
I hope this is at least partially helpful!
Matt in New York (up in Westchester!)
Matt H.
sure.
you found out the height of the smaller triangle by already knowing its area and its base. Since the formula for finding the area of a triangle is to multiply take 1/2 of the base times the height, you can also do it backwards: multiply the area x 2, then
divide that answer by the length of the base.
Once you got the height of the smaller triangle, you can use the ratio of 3:5 to get the height of the larger one. Why? Because if thr base of one triangle is 3, and the same base of the other triangle is 5, ALL of its dimensions will be in a 3:5 ratio.
We figured out the height of the first one was 4, so base 3 is to base 5 as height 4 is to height...
Set it up as a proportion: 3/5 = 4/h. That cross-multiplies to 3h = 20, so h = 6.66666... repeating.
I hope that helps!!
Cheers,
Matt
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01/08/15
Ash R.
01/08/15