SAT Math Question

[DaniNY1]

What is the greatest possible area of a triangle with one side of length 7 and the another side of length 10?


Choices:

A - 17
B - 34
C - 35
D - 70
E - 140

Answer is 35 but how?

Thanks in advance

 

[pka]

What is the greatest possible area of a triangle with one side of length 7 and the another side of length 10?


Choices:

A - 17
B - 34
C - 35
D - 70
E - 140

Answer is 35 but how?

Maximum areas occur in right triangles.

 

[DaniNY1]

Is there anyway to show how to "prove" this? I am teaching an SAT course and I just want to assure I can explain this as clear as possible

 

[Bob Brown MSEE]

Proof: Area is half the area of a Parallelogram, who's area is base times height.

 

[Deleted member 4993]

If the sides given AB and BC and the angle between them (ABC) is Θ, then

area of the triangle ABC = ½ * |AB| * |BC| * sin(Θ)

max value of sin(Θ) = 1 at Θ = π/2

Hence for max area mABC = π/2

 

[Deleted member 4993]

What is the greatest possible area of a triangle with one side of length 7 and the another side of length 10?


Choices:

A - 17
B - 34
C - 35
D - 70
E - 140

Answer is 35 but how?

Thanks in advance

This problem is incorrect. A third side with any of those above answers will not form a triangle with non-zero area(triangle inequality).

 

[lookagain]

This problem is incorrect. A third side with any of those above answers will not form a
triangle with non-zero area(triangle inequality).

Subhotosh Khan, those answer choices are for the area of the triangle, not the possible length of the third side.

The problem isn't incorrect.

 

[Deleted member 4993]

Got pinged by lookagain twice this morning (and deservedly so I must say) ....

Denis and SirMichael - are you guys still there in the corner .... can I join in??