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555-605 (Medium)|   Geometry|      
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Bunuel
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In a triangle with perimeter equal to 24, the side lengths are three 27 Oct 2020, 06:15
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80% (01:30) correct 20% (03:02) wrong based on 54 sessions

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In a triangle with perimeter equal to 24, the side lengths are three consecutive even integers. What is the triangle’s area?

A. 8
B. 12
C. 16
D. 20
E. 24
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E
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In a triangle with perimeter equal to 24, the side lengths are three 27 Oct 2020, 08:08
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The side lengths form an equally spaced list, so their median equals their average, which is 24/3 = 8. So the side lengths are 6, 8 and 10. Since this is a 3-4-5 triangle, it's a right triangle, so we can use its two short sides as base and height, and the area is 6*8/2 = 24.
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In a triangle with perimeter equal to 24, the side lengths are three 27 Oct 2020, 08:48
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Let the sides be x, x + 2 and x + 4

Then x + x + 2 + x + 4 = 24

3x = 18 or x = 6

The sides are 6,8 and 10. This a pythagorean triplet and therefore the base and height are the 2 smaller sides.

Area = 1/2 * base * height = 1/2 * 6 * 8 = 24


Option E

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In a triangle with perimeter equal to 24, the side lengths are three 27 Oct 2020, 08:50
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let one side of the triangle be n
then the other 2 sides will be n+2 & n+4

n+(n+2)+(n+4) = 24
n = 6

sides are 6,8,10. This is in proportion with 3-4-5 triangle. So, this is a right angle triangle.
So, we can take 6 & 8 as short leg and long leg.

Area of a triangle = 1/2 * base * height

= 1/2 * 6 * 8 = 24

Answer E
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In a triangle with perimeter equal to 24, the side lengths are three 27 Oct 2020, 08:53
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Let's say sides are x-2, x, and x+2 for easier calculation.

X-2+X+X+2= 24

hence X= 8

So sides will be 6,8,10

which is a right angle triangle with sides . ( 6,8,10 )

Hence area will be 1/2 * 6* 8 = 24

Hence option E



Bunuel
In a triangle with perimeter equal to 24, the side lengths are three consecutive even integers. What is the triangle’s area?

A. 8
B. 12
C. 16
D. 20
E. 24
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In a triangle with perimeter equal to 24, the side lengths are three 16 Apr 2023, 10:04
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