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Difficulty:
65%
(hard)
Question Stats:
54% (02:16) correct
46%
(02:03)
wrong
based on 134
sessions
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The right triangle △ABC has side lengths 10 – x, 9 – x, and 8 – x. Given that only one value of x is possible, which of the following statements is true?
a) x is not an integer
b) The perimeter of △ABC must be greater than 10.
c) △ABC is isosceles
d) The area of △ABC cannot be determined from the information given
e) None of the above statements is true
a) x is not an integer
b) The perimeter of △ABC must be greater than 10.
c) △ABC is isosceles
d) The area of △ABC cannot be determined from the information given
e) None of the above statements is true
12 Feb 2019, 01:18
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amresh09
10-x, 9-x and 8-x are sequential numbers. They immediately remind one of 3-4-5 pythagorean triplet. If x = 5, we get the sides as 3-4-5.
The perimeter will be 3+4+5 = 12 which is greater than 10.
Answer (B)
KanishkM
Joined: 09 Mar 2018
Last visit: 18 Dec 2021
Posts: 755
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Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
amresh09
My thoughts on this, first thing which i thought after reading right triangle △ABC, the first Pythagorean triplet 3,4,5
Given that only one value of x is possible
Now Question is which of the following statements is true.
a) x is not an integer
As per my initial assumption this is not true.
b) The perimeter of △ABC must be greater than 10.
perimeter, sum of all sides => 27-3x > 10
we can take x as 5
12> 10
This is true
c) △ABC is isosceles
It can be possible, it cannot be possible
d) The area of △ABC cannot be determined from the information given
This for sure was false
e) None of the above statements is true
Irrelevant
