Question

Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer then how many such triangles exist? 1 point

Answer 1

Answer:

only one triangle exist in the place of x we can substitute 17 only...(8,15, 17) pythogarian triplet

Step-by-step explanation:

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Answer 2

• If x is an integer total 10 such triangles exist .

Given :- An obtuse-angled triangles with sides 8 cm, 15 cm and x cm . where x is an integer .

To Find :- How many such triangles exist ?

Formula / Concept used :-

• Sum of any two sides of a ∆ is greater than the third side .
• Difference between any two sides of a ∆ is smaller than the third side .
• In an obtuse - angled triangle with sides as a, b and c if c is side opposite to obtuse angle then, a² + b² < c² .

Solution :-

Case 1) :- Sum of any two sides of a ∆ is greater than the third side .

So,

→ 15 + 8 > x

→ 23 > x ------ (1)

Case 2) :- Difference between any two sides of a ∆ is smaller than the third side .

So,

→ 15 - 8 < x

→ 7 < x ----- (2)

from (1) and (2) we can conclude that,

→ 7 < x < 23 ------ (3)

Case 3) :- Let us assume that 15 cm as side opposite to obtuse angle then it will be greatest .

So,

→ 8² + x² < 15²

→ x² < 225 - 64

→ x² < 161

now, using (3) also :-

→ Possible values of x can be = 8, 9, 10, 11, 12 = Total 5 values .

Case 4) :- Let us assume that x cm as side opposite to obtuse angle then it will be greatest .

So,

→ 8² + 15² < x²

→ 289 < x²

again using (3) :-

→ Possible values of x can be = 18,19,20,21,22 = Total 5 values .

Hence, we can conclude that,

→ Total values possible for x (where x is an integer) = 5 + 5 = 10 (Ans.)

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