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505-555 (Easy)|   Geometry|      
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Bunuel
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The area of a right triangle whose sides are 6, 8, and 10 is how many 29 Nov 2018, 01:21
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C
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73% (00:38) correct 27% (00:32) wrong based on 79 sessions

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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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C
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The area of a right triangle whose sides are 6, 8, and 10 is how many Updated on: 29 Nov 2018, 21:18
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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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)
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The area of a right triangle whose sides are 6, 8, and 10 is how many 29 Nov 2018, 03:57
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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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The area of a right triangle whose sides are 6, 8, and 10 is how many 29 Nov 2018, 04:17
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Bunuel
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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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 Updated on: 15 Dec 2018, 14:22
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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sreejitb
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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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.
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The area of a right triangle whose sides are 6, 8, and 10 is how many 15 Dec 2018, 12:52
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sreejitb
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.
Show more

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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The area of a right triangle whose sides are 6, 8, and 10 is how many 15 Dec 2018, 14:22
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sreejitb
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sreejitb
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)}
Show more

Oh great thank you! A formula very less popular but can help in a trap.
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The area of a right triangle whose sides are 6, 8, and 10 is how many 21 Jul 2020, 10:49
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Bunuel
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
Show more

Asked: 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?

Area of a right triangle whose sides are 6, 8, and 10 = 1/2 * 6*8 = 24

Area of a right triangle whose sides are 3, 4, and 5 = 1/2 * 3 *4 = 6

Number of times = 24/6 = 4

IMO C
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