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.