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harsh.champ
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Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?
(A)13
(B)21
(C)10
(D)15
(E)14
The OA is C. 10
Don't look at the soln before answering by yourself.
Solution:-
[spoiler]We know that for an obtuse triangle of sides a, b and c (where c is the largest side),
a2 + b2 < c2
We also know that for a triangle, a + b > c
These present us with two limiting cases.
Let 8 cm and 15 cm be the length of shorter sides. The value of the largest side (x) must be greater than sqrt(8^2 + 15^2) which is 17cm.
The possible integer values of x are 18, 19, 20, 21 and 22 cm.
We cannot consider values from 23 onwards because 8 + 15 = 23 and this violates the second condition.
Now, consider the case where 15 cm is the measure of the largest side.
The value of the remaining side (x) must be less than sqrt(15^2 - 8^2) which is 12.69 cm.
The possible integer values are 12, 11, 10, 9 and 8 cm.
We cannot consider values less than 8 because 7 + 8 = 15 and this violates the second condition.
Thus, we have in total 10 possible values for x. Hence, option C.[/spoiler]
Just try it out.
(A)13
(B)21
(C)10
(D)15
(E)14
The OA is C. 10
Don't look at the soln before answering by yourself.
Solution:-
[spoiler]We know that for an obtuse triangle of sides a, b and c (where c is the largest side),
a2 + b2 < c2
We also know that for a triangle, a + b > c
These present us with two limiting cases.
Let 8 cm and 15 cm be the length of shorter sides. The value of the largest side (x) must be greater than sqrt(8^2 + 15^2) which is 17cm.
The possible integer values of x are 18, 19, 20, 21 and 22 cm.
We cannot consider values from 23 onwards because 8 + 15 = 23 and this violates the second condition.
Now, consider the case where 15 cm is the measure of the largest side.
The value of the remaining side (x) must be less than sqrt(15^2 - 8^2) which is 12.69 cm.
The possible integer values are 12, 11, 10, 9 and 8 cm.
We cannot consider values less than 8 because 7 + 8 = 15 and this violates the second condition.
Thus, we have in total 10 possible values for x. Hence, option C.[/spoiler]
Just try it out.
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Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.
"Keep Walking" - Johnny Walker
Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.
"Keep Walking" - Johnny Walker
