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Basic Proportionality Theorem

ABC, m∠ B=45 ...

Question

$△ A B C, m ∠ B = 45$ and $¯ ¯¯¯¯¯¯¯¯ ¯ A M$ is an altitude, $M \in ¯ ¯¯¯¯¯¯ ¯ B C$ . If $B C = 7$ and $A M = 4$ then $A C =$ ______

A

4

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B

2.5

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C

5

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D

10

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Solution

The correct option is C $5$
$\begin{matrix} I n Δ A B M ∠ A = 180^{0} - 90^{0} - 45^{0} = 45^{0} ∠ A = ∠ B = 45^{0} B M = A M = 4 c m M C = 7 - 14 c m = 3 c m I n Δ A M C A C^{2} = M C^{2} + A M^{2} = 3^{2} + 4^{2} = 25 A C = 5 c m \end{matrix}$

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Similar questions

△ A B C

A B C = 45^{o}

A M ⊥ B C

A M = 4 c m

B C = 7 c m

. Find the length of

A C

Δ A B C, ∠ B = 45

¯ ¯¯¯¯¯¯¯¯ ¯ A M ⊥ ¯ ¯¯¯¯¯¯ ¯ B C \cdot

If B C = 7 , A M = 4 then A C =

△ A B C, ∠ A B C = 90^{o}

and BM is the altitude. If AM = 16 MC Prove that

AB = 4 BC

△ A B C, m ∠ B = 90^{o}, ¯ ¯¯¯¯¯¯¯¯ ¯ B M ⊥ ¯ ¯¯¯¯¯¯ ¯ A C, M \in A C

A M - M C = 7

{A B}^{2} - {B C}^{2} = 175

A C

△ A B C

A B = 4

A C = 8

cm. If M is the midpoint of BC and

A M = 3

cm, then the length of

B C

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