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Question
The ratio of the areas of two triangles with the common base is 4 : 3. Height of the larger triangle is 2 cm, then find the corresponding height of the smaller triangle.
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Solution
Let the height of the larger triangle be h1 and that of the smaller triangle be h2.
The ratio of the areas of two triangles with a common base is equal to the ratio of their corresponding heights.
`"Area(larger Triangle)"/"Area(smaller Triangle)"="h"_1/"h"_2`
`4/3=2/"h"_2`
`4xx "h"_2=3xx2`
`therefore"h"_2=(3xx2)/4=6/4`
`therefore"h"_2=1.5" cm"`
The corresponding height of the smaller triangle is 1.5 cm.
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In the figure, PQ ⊥ BC, AD ⊥ BC. To find the ratio of A(ΔPQB) and A(ΔPBC), complete the following activity.
Given: PQ ⊥ BC, AD ⊥ BC
Now, A(ΔPQB) = `1/2 xx square xx square`
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= `square/square`
