Question

the perimeter of two similar triangles ABC and PQR are 25cm and 15cm respectively. If one side of the first triangle is 9cm. Find the corresponding side of another triangle

Answer 1

The answer is: " 5
`(2)/(5)` cm " ;

or, write as: " 5. 4 cm " .

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25/15 = 9 /x ;

Reduce the "25/15 " :

→ " (25/15) = (25÷5) / (15÷5) = "(5/3)" ;

→ And rewrite:

→ 5 / 3 = 9 / x ;

Cross-multiply:

→ 5 x = 3 * 9 ;

→ 5x = 27 ;

Divide each side of the equation by "5" ; as follows:

→ 5x / 5 = 27 / 5 ;

to get ;

→ x = 27 / 5 ;

= {27 ÷ 5} ;

→ x = " 5
`(2)/(5)` cm " ;

or, write as: " 5. 4 cm " .

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Answer 2

If two triangles are similar, then all the corresponding sides and perimeter are in the same ratio.

Given that ∆ABC and ∆PQR are similar,

perimeter of ∆ABC = 25cm

perimeter of ∆PQR = 15 cm

One side of ABC = 9cm

Let corresponding side of PQR = x


`(x)/(9) = (15)/(25) \\ \\ x = (15)/(25) * 9 = (27)/(5) \: cm = 5.4 \: cm`

Corresponding side is 5.4 cm