Q. 6 A5.0( 1 Vote )

Fill in the blanks so that the following statements are true:

and are the altitudes of ΔABC. If AB = 12, AC = 9.9, AD = 8.1 and BE = 7.2, perimeter of ΔABC = _____.

Answer :

We have

Given that: AD and BE are altitudes of ∆ABC. ADC =

In ∆ADC and ∆BEC,

ADC = BEC [, ADC = BEC = 90° as AD and BE ]

ACD = BCE [, ACD and BCE are same angles of the same triangles, so they obviously are equal]

By AA-corollary, we can say that ∆ADC ∆BEC for the correspondence of ADC BEC.

By definition, for a given correspondence between the vertices of two triangles, if the corresponding angles of the triangles are congruent and the lengths of the corresponding sides are in proportion, then the given correspondence is a similarity between two triangles.

BC = 8.8

So, perimeter of ∆ABC is given by

Perimeter of ∆ABC = AB + BC + AC

Perimeter of ∆ABC = 12 + 8.8 + 9.9

Perimeter of ∆ABC = 30.7

Thus, perimeter of ∆ABC = 30.7.

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