#### The areas of two similar triangles are 81 and 49 cm^2 respectively. If the altitude of the bigger triangle is 4.5 cm. Find the corresponding attitude for the smaller triangle.

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similar triangles
Q.A1.CT.26.2
Mathematics
The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
word problem
High-school syllabus questions

Anonymous

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Krishna

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Step 1: Recall the relation between the areas of the similar triangles.

THEOREM: The ratio of the areas of two similar triangles is equal to the

ratio of the squares of their corresponding sides

\frac{Area \triangle ABC}{Area \triangle DEF} = (\frac{AB}{DE})^2 = (\frac{BC}{EF})^2 = (\frac{CA}{FD})^2

And also, \frac{Area\ \triangle ABC}{Area\ \triangle DEF}=(\frac{Altitude\ 1}{Altitude\ 2})^2

Step 2: Substitute all the known values in the theorem

EXAMPLE: \frac{81}{49}=(\frac{4.5}{Altitude\ 2})^2

\Rightarrow\ Altitude\ 2\ =\ \sqrt{\left(4.5\right)^2\cdot\frac{49\ }{81}}

\Rightarrow Altitude\ 2\ =\ 4.5\ \frac{7}{9}

Altitude of a smaller triangle = 3.5 cm