मराठी
महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

In the following figure RP : PK= 3 : 2, then find the value of A(ΔTRP) : A(ΔTPK).

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प्रश्न

In the following figure RP : PK= 3 : 2, then find the value of A(ΔTRP) : A(ΔTPK).

बेरीज
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उत्तर

Ratio of the areas of two triangles with common or equal heights is equal to the ratio of their corresponding bases.

`(A(triangleTRP))/(A(triangleTPK))`

`="RP"/"PK"`

`=3/2`

A(△TRP) : A(△TPK) = 3 : 2​
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2013-2014 (March)

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In fig., TP = 10 cm, PS = 6 cm. `(A(ΔRTP))/(A(ΔRPS))` = ?


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ΔPQS and ΔQRS having seg QS common base.

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


From adjoining figure, ∠ABC = 90°, ∠DCB = 90°, AB = 6, DC = 8, then `(A(ΔABC))/(A(ΔBCD))` = ?


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:

  1. Draw two triangles, give the names of all points, and show heights.
  2. Write 'Given' and 'To prove' from the figure drawn.

If ΔABC ∼ ΔDEF, length of side AB is 9 cm and length of side DE is 12 cm, then find the ratio of their corresponding areas.


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