Question

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

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

Answer 1

The correct option is A

An acute-angled triangle

The angles of a triangle are of the ratio $5:3:7$

Let the angles of a triangle be $5x,3x$ and $7x$

Using the angle sum property of a triangle,

$$\begin{gathered} \Rightarrow 5x+3x+7x=180 \\ \Rightarrow 15x=180 \\ \Rightarrow x=\frac{180}{15} \\ \Rightarrow x=12 \end{gathered}$$

On Substituting the value of $x=12,in$

$$\begin{gathered} 5x=5\times 12=60° \\ 7x=7\times 12=84° \\ 3x=3\times 12=36° \end{gathered}$$

Since all the angles are less than $90°$, the triangle is an acute-angled triangle.

Therefore, option (A) is the correct answer.