Question

areas of two similar triangles are 5 centimetre square 9 centimetre square one side of bigger triangle is 3 cm find the corresponding side of the smaller Triangle

Answer 1

Answer:

√5 cm

Step-by-step explanation:

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Answer 2

Answer:-

$\sf{The \ corresponding \ side \ of \ smaller \ triangle}$

$\sf{is \ \sqrt5 \ cm}$

Given:

• $\sf{\triangle_{1} \ \sim \ \triangle_{2}}$

• $\sf{A(\triangle_{1})=5 \ cm^{2}}$

• $\sf{A(\triangle_{2})=9 \ cm^{2}}$

• $\sf{Side \ of \ bigger \ triangle=3 \ cm}$

To find:

• The corresponding side of the similar triangle.

Solution:

$\sf{Let \ the \ corresponding \ side \ of \ smaller \ triangle \ be \ x}$

$\sf{By \ theorem \ of \ area \ of \ similar \ triangles.}$

$\sf{\frac{A(\triangle_{1})}{A(\triangle_{2})}=Ratio \ of \ squares \ of \ corresponding \ sides.}$

$\sf{\therefore{\frac{A(\triangle_{1})}{A(\triangle_{2})}=\frac{x^{2}}{3^{2}}}}$

$\sf{\therefore{\frac{5}{9}=\frac{x^{2}}{9}}}$

$\sf{\therefore{x^{2}=5}}$

$\sf{\therefore{x=\sqrt5}}$

$\sf\purple{\tt{\therefore{The \ corresponding \ side \ of \ smaller}}}$

$\sf\purple{\tt{triangle \ is \ \sqrt5 \ cm}}$