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प्रश्न
In the given figure, BC ⊥ AB, AD ⊥ AB, BC = 4, AD = 8, then find `("A"(∆"ABC"))/("A"(∆"ADB"))`
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उत्तर
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`.
संबंधित प्रश्न
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Areas of two triangles whose base is common are in proportion of their corresponding `square`.
`(A(ΔPQS))/(A(ΔQRS)) = (square)/(NR)`,
`100/110 = (square)/(NR)`,
NR = `square` cm
Prove that, The areas of two triangles with the same height are in proportion to their corresponding bases. To prove this theorem start as follows:
- Draw two triangles, give the names of all points, and show heights.
- Write 'Given' and 'To prove' from the figure drawn.
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`
