Question

The angles of a triangle are in the ratio $5:3:7$. The triangle is __________.

• A. Acute angled
• B. Obtuse angled
• C. Right angled
• D. Isosceles

Answer 1

Answer: (A)

Acute angled

Let the angle of triangle be $5x,3x,7x$

Now,

$\because$ Sum of angles of Triangle is ${180}^{\circ }$

$\therefore 5x+3x+7x={180}^{\circ }$

$⟹15x={180}^{\circ }$

$⟹x=\frac{{180}^{\circ }}{15}$

$⟹x={12}^{\circ }$

Hence, Angle of the triangle are

$5x=5\times {12}^{\circ }={60}^{\circ }$

$3x=3\times {12}^{\circ }={36}^{\circ }$

$7x=7\times {12}^{\circ }={84}^{\circ }$

Since, All the angle of the trianle is less than ${90}^{\circ }$

Therefore, Triangle is Acute angled.