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Maharashtra State BoardSSC (English Medium) 10th Standard

In the given figure, BC ⊥ AB, AD ⊥ AB, BC = 4, AD = 8, then find AABCAADBA(∆ABC)A(∆ADB)

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Question

In the given figure, BC ⊥ AB, AD ⊥ AB, BC = 4, AD = 8, then find `("A"(∆"ABC"))/("A"(∆"ADB"))`

Sum
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Solution

In ∆ABC and ∆ADB,
BC ⊥ AB, AD ⊥ AB, BC = 4, AD = 8   ...(Given)

∆ABC and ∆ADB have same base AB. ...(Given)

∴ Areas of triangles with equal bases are proportional to their corresponding heights.

`("A"(∆"ABC"))/("A"(∆"ADB")) = "BC"/"AD"`

∴ `("A"(∆"ABC"))/("A"(∆"ADB")) = 4/8`

∴ `("A"(∆"ABC"))/("A"(∆"ADB")) = 1/2`.

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Chapter 1: Similarity - Practice Set 1.1 [Page 6]

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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`

A(ΔPBC)  = `1/2 xx square xx square`

Therefore, 

`(A(ΔPQB))/(A(ΔPBC)) = (1/2 xx square xx square)/(1/2 xx square xx square)`

= `square/square`


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