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# The area of a right triangle whose sides are 6, 8, and 10 is how many

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Math Expert
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The area of a right triangle whose sides are 6, 8, and 10 is how many  [#permalink]

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29 Nov 2018, 01:21
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The area of a right triangle whose sides are 6, 8, and 10 is how many times the area of a right triangle whose sides are 3, 4, and 5?

A. 2
B. 3
C. 4
D. 6
E. 8

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The area of a right triangle whose sides are 6, 8, and 10 is how many  [#permalink]

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Updated on: 29 Nov 2018, 21:18
Area of triangle with sides 6,8,10 = 0.5 * 6 * 8 = 24. Area of triangle with sides 3,4,5 = 0.5 * 3 * 4 = 6. Ratio = 24/6 = 4.(Option C)

Originally posted by rahulsinha2103 on 29 Nov 2018, 01:41.
Last edited by rahulsinha2103 on 29 Nov 2018, 21:18, edited 1 time in total.
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Re: The area of a right triangle whose sides are 6, 8, and 10 is how many  [#permalink]

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29 Nov 2018, 03:57
1
Semi Perimeter of First Triangle = (6 + 8 + 10)/2 = 12
Area = \sqrt{S (S-6)(S-8)(S-10)} = 24.

Semi Perimeter of First Triangle = (3 + 4 + 5)/2 = 6
Area = \sqrt{S (S-3)(S-4)(S-5)} = 6.

Ratio of Areas = 24/6 = 4.

Hence, C.
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Re: The area of a right triangle whose sides are 6, 8, and 10 is how many  [#permalink]

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29 Nov 2018, 04:17
Bunuel wrote:
The area of a right triangle whose sides are 6, 8, and 10 is how many times the area of a right triangle whose sides are 3, 4, and 5?

A. 2
B. 3
C. 4
D. 6
E. 8

so area of the triangle would be
1/2*6*8= 24 and 1/2*4*3 = 6 which is 4 times IMO C
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The area of a right triangle whose sides are 6, 8, and 10 is how many  [#permalink]

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Updated on: 15 Dec 2018, 14:22
sreejitb wrote:
Semi Perimeter of First Triangle = (6 + 8 + 10)/2 = 12
Area = \sqrt{S (S-6)(S-8)(S-10)} = 24.

Semi Perimeter of First Triangle = (3 + 4 + 5)/2 = 6
Area = \sqrt{S (S-3)(S-4)(S-5)} = 6.

Ratio of Areas = 24/6 = 4.

Hence, C.

Could you please explain the use of the formula in detail? Because I think this is a better use if we do not know what side of the triangle is base and what is the height. In this case we had popular combinations of sides.

Originally posted by seeker14 on 15 Dec 2018, 12:02.
Last edited by seeker14 on 15 Dec 2018, 14:22, edited 1 time in total.
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Re: The area of a right triangle whose sides are 6, 8, and 10 is how many  [#permalink]

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15 Dec 2018, 12:52
2
seeker14 wrote:
sreejitb wrote:
Semi Perimeter of First Triangle = (6 + 8 + 10)/2 = 12
Area = \sqrt{S (S-6)(S-8)(S-10)} = 24.

Semi Perimeter of First Triangle = (3 + 4 + 5)/2 = 6
Area = \sqrt{S (S-3)(S-4)(S-5)} = 6.

Ratio of Areas = 24/6 = 4.

Hence, C.

Could you please explain the use of the formula in detail? Because I think this is a better use of we do not know what side of the triangle is base and what is the height. In this case we had popular combinations of sides.

This is what is called the "Heron's Formula". This formula gives us the area of a triangle when the length of all three sides are known.
Let the 3 sides of a triangle be of length a, b and c.
Hence perimeter (P) = a + b + c
Semi Perimeter (P/2) = (a + b + c)/2. Say "S".

Hence Area (A) of the triangle will be:

A = \sqrt{S(S-a) (S-b) (s-c)}
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Re: The area of a right triangle whose sides are 6, 8, and 10 is how many  [#permalink]

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15 Dec 2018, 14:22
sreejitb wrote:
seeker14 wrote:
sreejitb wrote:
Semi Perimeter of First Triangle = (6 + 8 + 10)/2 = 12
Area = \sqrt{S (S-6)(S-8)(S-10)} = 24.

Semi Perimeter of First Triangle = (3 + 4 + 5)/2 = 6
Area = \sqrt{S (S-3)(S-4)(S-5)} = 6.

Ratio of Areas = 24/6 = 4.

Hence, C.

Could you please explain the use of the formula in detail? Because I think this is a better use of we do not know what side of the triangle is base and what is the height. In this case we had popular combinations of sides.

This is what is called the "Heron's Formula". This formula gives us the area of a triangle when the length of all three sides are known.
Let the 3 sides of a triangle be of length a, b and c.
Hence perimeter (P) = a + b + c
Semi Perimeter (P/2) = (a + b + c)/2. Say "S".

Hence Area (A) of the triangle will be:

A = \sqrt{S(S-a) (S-b) (s-c)}

Oh great thank you! A formula very less popular but can help in a trap.
Re: The area of a right triangle whose sides are 6, 8, and 10 is how many   [#permalink] 15 Dec 2018, 14:22
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