Question

# Fill in the blanks:The perimeters of two similar triangles are 25cm and 15cm respectively. If one side of the first triangle is 9cm, then the corresponding side of the second triangle is ………..

Hint: To solve this question, we will use the perimeter property of similar triangles which states that – The ratio of perimeters of two similar triangles is equal to the ratio of their corresponding sides that is
$\dfrac{{{P_1}}}{{{P_2}}} = \dfrac{{{a_1}}}{{{a_2}}}$ , where${P_1}$, ${P_2}$ and ${a_1}$and ${a_2}$are the perimeters and the corresponding sides of the two similar triangles respectively.

So, let the perimeter of the first triangle be${P_1}$=25 cm and the perimeter of the second triangle be ${P_2}$=15cm. Let one side of the first triangle be ${a_1}$=9cm, and the corresponding side of the second triangle be${a_2}$.
$\dfrac{{{P_1}}}{{{P_2}}} = \dfrac{{{a_1}}}{{{a_2}}}$
So, to find the value of ${a_2}$we will put the values of ${P_1}$=25, ${P_2}$=15cm and ${a_1}$=9cm, we will get the equation as:
$\dfrac{{25}}{{15}} = \dfrac{9}{{{a_2}}} \\ \Rightarrow \dfrac{5}{3} = \dfrac{9}{{{a_2}}} \\ \Rightarrow {a_2} = \dfrac{{3 \times 9}}{5} \\ \Rightarrow {a_2} = 5.4cm \\$