Question

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Answer 1

Given:

☯ ∠AMP = ∠ABC = 90°

☯ BC = a

☯ BM = v

☯ MA = c

To Express:

The value of x in terms of a, v, c

Solution:

In ∆APM and ∆ABC

➢ ∠AMP = ∠ABC = 90° ( given )

➢ ∠A = ∠A ( common )

∴ ∆APM ∼ ∆ABC [ By AA similarly criterion of triangles ]

Now, two triangles are said to be similar when the corresponding angles are equal and corresponding sides are proportional to each other i.e., the ratio between the lengths of of corresponding sides are equal.

Thus, corresponding sides of similar triangles are proportional.

➩ AM/AB = MP/BC [ corresponding sides of similar triangle are proportional ]

• AM = c

• AB = AM + MB
• AB = c + v

• MP = x

• BC = a

➟ c/(v + c) = x/a

➟ x = ac/ v + c

∴ x = ac/ v + c

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Answer 2

Answer:

$x=\frac{ac}{b+c}$

Refer the attachment☺