Question

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

• A. An isosceles triangle
• B. An acute angled triangle
• C. An obtuse angled triangle
• D. A right triangle

Answer 1

The correct option is B

An acute angled triangle

The sum of all the three angles of a triangle = 180${}^{\circ }$

Since the angles are in the ratio 5:3:7, let x be a factor such that,

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

$\Rightarrow$ $15x$ =180${}^{\circ }$

$\Rightarrow$ $x$ =12${}^{\circ }$

Hence the three angles of the triangle are:

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

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

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

Since all the angles in the triangle are less than ${90}^{\circ }$, the triangle is an acute angled triangle.