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Bunuel
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What is the maximum possible area of a triangle with a side of length 25 Mar 2021, 07:00
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C
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70% (01:07) correct 30% (01:18) wrong based on 80 sessions

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What is the maximum possible area of a triangle with a side of length 7 units and another side of length 8 units?

A. 14 square units

B. 21 square units

C. 28 square units

D. 56 square units

E. 64 square units
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C
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What is the maximum possible area of a triangle with a side of length 25 Mar 2021, 09:14
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Bunuel
What is the maximum possible area of a triangle with a side of length 7 units and another side of length 8 units?

A. 14 square units

B. 21 square units

C. 28 square units

D. 56 square units

E. 64 square units
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We can treat 8 as the base, if 7 were to be another length of the triangle then the highest area possible is when 7 is the height. Any other angle between 8 and 7 that is not a right angle, results in a height less than 7. Then the area is \(8*7/2 = 28\).

Ans: C
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aniruddhawarang29
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What is the maximum possible area of a triangle with a side of length 27 Mar 2021, 05:05
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Bunuel
What is the maximum possible area of a triangle with a side of length 7 units and another side of length 8 units?

A. 14 square units

B. 21 square units

C. 28 square units

D. 56 square units

E. 64 square units

We can treat 8 as the base, if 7 were to be another length of the triangle then the highest area possible is when 7 is the height. Any other angle between 8 and 7 that is not a right angle, results in a height less than 7. Then the area is \(8*7/2 = 28\).

Ans: C
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But why is the third side not considered here?

The third side can be in the range of 1<x<15.

For the area to be max the base and height need to be max numbers of these three i.e 7,8 and 14

So area comes out to be 8*14/2 = 56.

Pls rectify if I am not on the right track.
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What is the maximum possible area of a triangle with a side of length 05 Jun 2021, 11:58
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Bunuel
What is the maximum possible area of a triangle with a side of length 7 units and another side of length 8 units?

A. 14 square units

B. 21 square units

C. 28 square units

D. 56 square units

E. 64 square units

We can treat 8 as the base, if 7 were to be another length of the triangle then the highest area possible is when 7 is the height. Any other angle between 8 and 7 that is not a right angle, results in a height less than 7. Then the area is \(8*7/2 = 28\).

Ans: C




But why is the third side not considered here?

The third side can be in the range of 1<x<15.

For the area to be max the base and height need to be max numbers of these three i.e 7,8 and 14

So area comes out to be 8*14/2 = 56.

Pls rectify if I am not on the right track.
Show more

You can intuitively imagin that when you make the third side bigger, the height of the triangle is smaller and then the area is smaller (obviously it won't be a right triangle). You can also see that the same happens when the third side is small.
Using Heron's formula of the area of a triangle using lengths of the sides we have:
A = 0,25*sqrt(−x^4+226x^2−225)
being x the length of the third side.
If you draw that function you can see that the maximum is at x = sqrt(113). Which is the same length that we obtain supposing that it is a right triangle with x as the hypotenuse.
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