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Heights & Distances

Condition for...

Question

Condition for an acute-angled triangle with sides $a$ , $b$ , and $c$ is
$a^{2} + b^{2} > c^{2}$ (where $c$ is the longest side).
If $y$ is an integer, then how many acute-angled triangles with sides $7 c m$ , $12 c m$ , and $y c m$ exist?

2

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4

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3

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Infinite

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Solution

The correct option is C $3$

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Similar questions

a^{2} + b^{2} > c^{2}

Question 7

Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is

a) Obtuse-angled triangle
b) Acute angled triangle
c) Right angled triangle
d) An isosceles right triangle.

The side opposite to acute angles of a right angled triangle are 7 cm and 24 cm, the side opposite to right angle is

14 c m

18 c m

20 c m

θ

a

b

c

A

B

C

\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}

c^{2} = a^{2} + b^{2} - 2 a b cos C

\to x

\to y

A B C

a, b

c

(20 a - 15 b) \to x + (15 b - 12 c) \to y + (12 c - 20 a) (\to x \times \to y) = \to 0

A B C

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