Question

Perimeter of two similar triangles are 25cm and 15cm respectively. If one side of first triangle is 9cm. find length of corresponding side of second triangle​

Answer 1

Answer:

The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of the first triangle is 9 cm, then the corresponding side of second triangle is 5.4 cm.

Step-by-step explanation:

Answer 2

Perimeters of two similar triangles are 25cm and 15cm respectively.

One side of first triangle = 9cm

\begin{gathered}\\\end{gathered}

★To find:-

The length of the corresponding side of the second triangle.

★Solution:-

\begin{gathered}\\\end{gathered}

Let the two similar triangle are ΔABC &ΔPQR

As, ΔABC is similar to ΔPQR,

\leadsto \underline{\boxed{\sf Ratio \ of\ perimeter\ of\ \triangle 's=Ratio\ of\ corresponding\ sides}}⇝

Ratio of perimeter of △

′

s=Ratio of corresponding sides

\begin{gathered}:\implies \sf \dfrac{25}{15} =\dfrac{AB}{PQ} \\\\\\:\implies \sf \dfrac{25}{15} =\dfrac{9}{PQ} \\\\\\:\implies \sf PQ = \dfrac{15\times 9}{25} \\\\\\:\implies \underline{\boxed{\sf PQ=5.4cm.}}\\\\\end{gathered}

:⟹

15

25

=

PQ

AB

:⟹

15

25

=

PQ

9

:⟹PQ=

25

15×9

:⟹

PQ=5.4cm.

Hence,

The length of corresponding side of second triangle is 5.4cm.

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Know More:-

\begin{gathered}\\\end{gathered}

✦Two or more triangles are said to be similar when they have same shape, equal pair of corresponding angles & the same ratio of the corresponding sides.

Rules of similarity:-

✦Angle-Angle(AA) rule:

Two triangles are said to be similar if two angles in one triangle are equal to two angles of another triangle.

✦Side-Angle-Side (SAS) rule:

The ratio of their corresponding two sides is equal and the angle formed by two sides is also equal.

✦Side-Side-Side (SSS) rule:

All the corresponding three sides of the given triangles are in equal proportion.

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