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In right triangle, ABC, the ratio of the longest side to the shortest
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23 May 2019, 04:03
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55% (02:01) correct 45% (02:14) wrong based on 31 sessions
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In right triangle, ABC, the ratio of the longest side to the shortest side is 5 to 3. If the area of ABC is between 50 and 150 (50 and 150 not inclusive), which of the following could be the length of the shortest side? I. 9 II. 12 III. 15 A. I only B. II only C. III only D. I and II only E. I, II and III
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Re: In right triangle, ABC, the ratio of the longest side to the shortest
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23 May 2019, 04:21
Let longest side=5x and shortest side=3x Third side= [(5x)^2  (3x)^2]^1/2= 4x {Pythagoras Theorm}
Area= 1/2*4x*3x=6x^2
50<6x^2<150 75<9x^2<225 8.6<3x<15
Shortest side could be 9 or 12



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Re: In right triangle, ABC, the ratio of the longest side to the shortest
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23 May 2019, 04:25
Bunuel wrote: In right triangle, ABC, the ratio of the longest side to the shortest side is 5 to 3. If the area of ABC is between 50 and 150 (50 and 150 not inclusive), which of the following could be the length of the shortest side?
I. 9 II. 12 III. 15
A. I only B. II only C. III only D. I and II only E. I, II and III ABC is right angled triangle. Now ratio of sides 5x:4x:3x 50 < (1/2)*(3x)*(4X) < 150 100< 12 (x^2)< 300 8.abc < (x^2) < 25 x can be 3,4 I 9 possible II 12 possible III 15 not possible. Answer D.
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Re: In right triangle, ABC, the ratio of the longest side to the shortest
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23 May 2019, 04:29
If the triangle is a right triangle then the ratio of the sides should necessarily be 3:4:5 as it’s already said that the ratio of shortest side to longest side is 3:5
Now, If the two smaller sides are 3x and 4x, Area = 0.5*3x*4x = 6x^2
Now, let’s evaluate the options: If the smaller side is 9, the second side has to be 12 as the ratio is 3:4 So, the area is 0.5*9*12 = 54 which is within the given range. So, 9 can be the shortest side.
If the smaller side is 12, the second side has to be 16 as the ratio is 3:4 So, the area is 0.5*12*16 = 96 which is within the given range. So, 12 can be the shortest side.
If the smaller side is 15, the second side has to be 20 as the ratio is 3:4 So, the area is 0.5*15*20 = 150 which is not within the given range. So, 15 cannot be the shortest side.
Hence, only 9 and 12 are the possible values.
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Re: In right triangle, ABC, the ratio of the longest side to the shortest
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23 May 2019, 20:11
Bunuel wrote: In right triangle, ABC, the ratio of the longest side to the shortest side is 5 to 3. If the area of ABC is between 50 and 150 (50 and 150 not inclusive), which of the following could be the length of the shortest side?
I. 9 II. 12 III. 15
A. I only B. II only C. III only D. I and II only E. I, II and III so let the ratio be 5x and 3x since it is a rightangled triangle, so we have the third side as 4x ( \((3x^2 + 4x^2 = 5x^2\)) ) area becomes = \(1/2 * 3x * 4x\) = 6x^2 given 50 < 6x^2 < 150 we would need to key in integer values x could be 2 and 3 only to satisfy the condition. so answer is D



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Re: In right triangle, ABC, the ratio of the longest side to the shortest
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28 May 2019, 07:20
Bunuel wrote: In right triangle, ABC, the ratio of the longest side to the shortest side is 5 to 3. If the area of ABC is between 50 and 150 (50 and 150 not inclusive), which of the following could be the length of the shortest side?
I. 9 II. 12 III. 15
A. I only B. II only C. III only D. I and II only E. I, II and III Since triangle ABC is a right triangle with ratio of the longest side to the shortest side of 5 to 3, it must be a 345 right triangle. Let’s analyze the Roman numerals now (keep in mind that the area of a right triangle is ½ of the product of the length of the two legs). I. 9 If the shortest side (or leg) is 3 x 3 = 9, then the other leg is 4 x 3 = 12. Therefore, the area of the triangle would be ½(9)(12) = 54. This works since 54 is between 50 and 150. II. 12 If the shortest side (or leg) is 3 x 4 = 12, then the other leg is 4 x 4 = 16. Therefore, the area of the triangle would be ½(12)(16) = 96. This works since 96 is between 50 and 150. III. 15 If the shortest side (or leg) is 3 x 5 = 15, then the other leg is 4 x 5 = 20. Therefore, the area of the triangle would be ½(15)(20) = 150. This doesn’t work since 150 is NOT between 50 and 150. Answer: D
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Re: In right triangle, ABC, the ratio of the longest side to the shortest
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