area of triangle

[kanha81]

One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?


I 24
II 20
III 5

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

What do you think should be the possible answer? Where in the question does it ask for maxm area?

[vasbli]

1. Area=(hxb)/2 and have to assume one of the sides is equal to h.

Area=5x8/2=20, so 20 works fine

the 3rd side of the triangle must be > 8+5=13

Choice B

[Claret]

alright, 20 is one of the possible answers.. how did you eliminate the other two?

[scoobydooby]

the maximum area of a triangle with 2 given sides is when the triangle is a right angled triangle

so max area with given sides 5 and 8 are 1/2*5*8=20. so I is ruled out.

if III were to be true, base*height=10. we already have 5, so the 3rd side must be 2. no triangle is possible with 2, 5, 8 as the sum of 2 sides is not greater than the 3rd side.

only II remains. hence, B

[tohellandback]

IMO D.,
Scoodooby,
I think ur solution is not accurate. Its not the third side that need to be 2. Its the height of the triangle from the base with length 5.

The max area is 20. But then it can go on decreasing until zero.
Please check the attachment.

Thanks

[kanha81]

IMO D.,
Scoodooby,
I think ur solution is not accurate. Its not the third side that need to be 2. Its the height of the triangle from the base with length 5.

The max area is 20. But then it can go on decreasing until zero.
Please check the attachment.

Thanks

tohellandback,

can you please help me understand? I was trying plug n chug and ended with and [III] as the potential answers and thought [II] would not work because it failed-
i) sum of two sides greater than third side
ii) difference of two sides less than third side

what made you think of maxm area of triangle and how did you decide to have base as 5? Grateful if you can please explain your thought process.

Bunch of thanks.

[tohellandback]

kanha ,
check the attachment plz.
You see the height wil be max when it is a right triangles...once you move the perpendicular side from that position either clockwise or anticlockwise, the height begins to decrease.
It will continue to decrease until zero when it joins the base.

Hope it helps.

[kanha81]

kanha ,
check the attachment plz.
You see the height wil be max when it is a right triangles...once you move the perpendicular side from that position either clockwise or anticlockwise, the height begins to decrease.
It will continue to decrease until zero when it joins the base.

Hope it helps.

Thanks. I will keep that in mind. makes sense now. OA [spoiler][D][/spoiler]