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E
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Difficulty:
45%
(medium)
Question Stats:
55% (00:54) correct
45%
(00:42)
wrong
based on 141
sessions
History
Date
Time
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Not Attempted Yet
What is the area of Triangle ABC?
1) one side's length of Triangle ABC is 3, the other's length is 4.
2) Triangle ABC is a right triangle
1) one side's length of Triangle ABC is 3, the other's length is 4.
2) Triangle ABC is a right triangle
14 Jan 2017, 21:11
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hwang327
Please consider below attached image
Note that we have not told that sides must be integer,if so case 1 only prevails
Ans will then be A
but here we have case 2 also and thus side x can be another value calculated as shown in attachment
thus we have two areas of triangle possible for each case as Area =1/2* base *height
so both are insuff
Ans E
Attachments
triangle.png [ 5.16 KiB | Viewed 3353 times ]
14 Sep 2023, 05:36
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Quick approach:
We are tryna find the area of triangle ABC
1) one side's length of Triangle ABC is 3, the other's length is 4
This means that 1 < x < 7, we could draw many different triangles that fits this inequality, where we would get different areas. There's no need to calculate anything, once you see the previous mentioned analysis we can eliminate this answer choice
2) Triangle ABC is a right triangle
This gives us the type of triangle we're looking for, but we don't know anything about the sides of the triangle, therefore eliminate this answer choice as well
1/2) We know that one side = 3, other = 4, and last side = 1 < x < 7 (where x is the last side)
Let's create 2 right triangles
Triangle 1: this Right Triangle is in the form of 3:4:5 (where 3 and 4 are the legs, and 5 is the hypotenuse) this would give us an area of 6 (since 12/2 = 6)
Triangle 2: this Right Triangle is in the form of 3:√7:4 (where 3 and √7 are the legs, and 4 is the hypotenuse), notice that this would give us a totally different area which is not equal to 6 (our previous triangle)
Since we got 2 different values and not 1 unique value, our answer will be E
We are tryna find the area of triangle ABC
1) one side's length of Triangle ABC is 3, the other's length is 4
This means that 1 < x < 7, we could draw many different triangles that fits this inequality, where we would get different areas. There's no need to calculate anything, once you see the previous mentioned analysis we can eliminate this answer choice
2) Triangle ABC is a right triangle
This gives us the type of triangle we're looking for, but we don't know anything about the sides of the triangle, therefore eliminate this answer choice as well
1/2) We know that one side = 3, other = 4, and last side = 1 < x < 7 (where x is the last side)
Let's create 2 right triangles
Triangle 1: this Right Triangle is in the form of 3:4:5 (where 3 and 4 are the legs, and 5 is the hypotenuse) this would give us an area of 6 (since 12/2 = 6)
Triangle 2: this Right Triangle is in the form of 3:√7:4 (where 3 and √7 are the legs, and 4 is the hypotenuse), notice that this would give us a totally different area which is not equal to 6 (our previous triangle)
Since we got 2 different values and not 1 unique value, our answer will be E
