Question

the corresponding altitude of two similar triangles are 6cm and 9cm respectively. Find the ratio of their areas
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Answer 1

Answer:

SOLUTION :  

Given:

The corresponding altitudes of two similar triangles are 6 cm and 9 cm.

We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes.

ar(∆1/)ar(∆2) = (altitude1/ altitude2)²

ar(∆1)/ar(∆2) = (6/9)²

ar(∆1)/ar(∆2) = 36/81

ar(∆1)/ar(∆2) = 4/9

ar(∆1)/ar(∆2) = 4: 9

Hence, the ratio of the areas of two triangles is 4: 9.

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Answer 2

Answer :

• Ratio of their areas is 4:9

Explanation :

We are given that there are two similar triangles, and the altitude of these triangles are 6 cm and 9 cm. We have to find Ratio of their Areas.

We know that,

$\longrightarrow \sf{\dfrac{Area \: of \: 1st \: Triangle}{Area \: of \: 2nd \: Triangle} \: = \: \dfrac{(Side \: of \: 1st \: triangle)^2}{(Side \: of \: second \: triangle)^2}} \\ \\ \longrightarrow \sf{\dfrac{Area \: of \: 1st \: Triangle}{Area \: of \: second \: Triangle} \: = \: \dfrac{6^2}{9^2}} \\ \\ \longrightarrow \sf{Ratio \: = \: \dfrac{36}{81}} \\ \\ \longrightarrow \sf{Ratio \: = \: \dfrac{4}{9}} \\ \\ \underline{\underline{\sf{Ratio \: of \: their \: Areas \: is \: 4 \: : \: 9}}}$

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Two triangles are said to be similar. If they have equal sides or equal a angle. If any of two angles or sides are equal. Then we can say that the triangle is similar to another triangle which have equal sides or angles as first one.