Question

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

Answer 1

★Given:-

• Perimeters of two similar triangles are 25cm and 15cm respectively.
• One side of first triangle = 9cm

★To find:-

• The length of the corresponding side of the second triangle.​

★Solution:-

Let the two similar triangle are ΔABC &ΔPQR

As, ΔABC is similar to ΔPQR,

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

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

Hence,

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

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Know More:-

✦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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