Question

In a right angled triangle, the ratio of the shorter sides is 2:3. Find the ratio of the hypotenuse of the triangle to its perimeter. (Assume $\sqrt{13}$ = 3.5)

• A. 7: $\sqrt{13}$
• B. $\sqrt{13}$:7
  
• C. 7:17
• D. $\sqrt{13}$:10
  

Answer 1

The correct option is C

7:17

Consider right triangle ABC.

Since AB : BC = 2:3, let AB = 2x and BC = 3x.

Using Pythagoras theorem,

${AC}^2$ = ${AB}^2$ + ${BC}^2$

⇒ ${AC}^2$ = ${\left(2x\right)}^2$ + ${\left(3x\right)}^2$ = 13 $x^2$

⇒ AC = $\sqrt{13}x$ = $3.5x$ = $\frac{7}{2}x$

Now, perimeter of the triangle

= AC + AB + BC

= $2x$ + $3x$ + $\frac{7}{2}x$ = $\frac{17}{2}x$

Required ratio = $\frac{hypotenuse}{perimeter}$

= $\frac{\frac{7x}{2}}{\frac{17x}{2}}$ = $\frac{7}{17}$

Therefore, ratio of hypotenuse to perimeter is 7:17.