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 ………..

Answer 1

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.

Complete step-by-step answer:
According to the question, it is given that there are two similar triangles whose perimeters are 25 cm and 15 cm respectively and one of its corresponding sides is 9cm, so we need to find the value of the other corresponding side of the second triangle.
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${a_2}$.
Now, from the perimeter property of similar triangles we know that the ratio of perimeters of two similar triangles is equal to the ratio of their corresponding sides that is
$\dfrac{{{P_1}}}{{{P_2}}} = \dfrac{{{a_1}}}{{{a_2}}}$
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 \\
 $
 Therefore, the length of the corresponding side of the second triangle is 5.4cm.
Hence, we will fill up the blank of the given statement with 5.4cm.

Note: Just like the perimeter property there is the area property of proportionality as well for similar triangles, which states that the ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding sides