M16, #15

Vertices of a triangle have coordinates (-1,0), (4,0) and (0,A). Is the area of the triangle bigger than 15 ?

(1) A<3
(2) The triangle is right


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I cldnt understand the explanation given for second statement. Can anyone explain?

What explanation for S2 is trying to say is that if we know that the triangle is right then we can find the coordinates of the point (0,A). Thus, we'll have enough info to answer the question. There are only two possible triangles with S2. See the image below. Do you think we need to change the wording of the OE for S2? If yes, please tell us what exactly was confusing.

Hope this helps.

Adding this drawing to the OE will greatly help.

Added the image there.

I hate to be too demanding, but what are the steps to find find the coordinates of (0, A)?

Knowing that the triangle is right means that the right angle must be at the point D(0,A), see the picture attached by dzyubam.

Next, we know that line segment AD is perpendicular to the line segment BD, hence the slopes of these line segments must be negative reciprocals of each other.

Slope AD=\frac{A-0}{0-(-1)}=A;
Slope BD=\frac{A-0}{0-4}=\frac{A}{-4}.

As they must be negative reciprocals, then: A=-\frac{-4}{A} --> A^2=4 --> A=2 or -2.

Hope it's clear.

Vertices of a triangle have coordinates , and . Is the area of the triangle bigger than 15?
1. A<3
2. The triangle is right

stmt 1: we know that 1 side length will be 5 and other side will be less than 3 so the third side can be as big as 7.999 and as small as 2.1 so it is not sufficient

stmt 2: if the given triangle is right angle then one side which forms the hypotenuse is 5 so the other two sides will be less than 4. so definitely area of triangle has to be less than 15

so ans is B

Someone pl explain why A cannot be the answer? If we map the triangle on a coordinate plane we have the base on X-axis and apex on Y-axis. Going by formula: Area = 1/2 (base x height) we have the base as 5 units and in order to have the area bigger than 15 we need the height to be >6 units. S1 says A<3, so height of triangle is <3 too hence area is less than 15. S1 SUFFICIENT

From S2 we know the triangle is right hence if the side on X-axes is 5 units the other 2 sides will be 3 & 4 units. Again, area <15. S2 SUFFICIENT
If above are correct then answer is D. Comments welcome.

"A" could be -ve as well

Hope that helps!

Thanks Igor010....silly me, should have realised seeing the figure drawn above!

To get the value of A apply twice Pythagorean Theorem:
1^2+A^2+4^2+A^2=5^2, A=\pm2, area=5<15. Certainly, B.

1 is sufficient as well i think answer is D