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Standard VII

Mathematics

Pythagoras Theorem

In Δ ABC, B...

Question

In $Δ A B C$ , B is a right angle and $¯ ¯¯¯¯¯¯¯ ¯ B D$ is an altitude. If AB=8, and BC=6, find BD.

2.8 c m

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4.8 c m

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5.8 c m

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None of these

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Solution

The correct option is B $4.8 c m$
Area of $Δ A B C \Rightarrow \frac{1}{2} \times (B C) (A C) = \frac{1}{2} \times (A C) (B D)$

$\Rightarrow (B C) (A B) = (A C) (B D)$ .........(1)

ABC is right triangle

$A B^{2} + B C^{2} = A C^{2}$

$\Rightarrow 8^{2} + 6^{2} = A C^{2}$

$\Rightarrow A C = 10 c m$ ......(2)

Put (2) in (1)

$(6) \times (8) = (10) (B D)$

$B D = 4.8 c m$

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Similar questions

$∠ B$ is a right angle in $△ A B C$ and $¯ ¯¯¯¯¯¯¯ ¯ B D$ is an altitude to hypotenuse. $A B = 8$ cm and $B C = 6$ cm. Find the area of $△ B D C$

Δ A B C

is a right angled triangle right angled at

B

and

B D

is the altitude from

B

on side

A C

. If

B D = 9

cm and inradii of

Δ A B C, Δ A B D

and

Δ B C D

are

r_{1}, r_{2}

and

r_{3}

respectively, then

r_{1} + r_{2} + r_{3}

Q. In a

Δ A B C, A D

is the bisector of

∠ A,

meeting side

B C

D

.
If

A B = 3.5 c m,

A C = 4.2 c m

and

D C = 2.8 c m

,
Find

B D

Q. Construct an isosceles triangle

A B C

in which base

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and altitude from

A

B C

4.8 c m

In a $Δ A B C$ , AD is the bisector of $∠ A$ , meeting side BC at D.
(i) If BD= 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD= 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB= 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB =10 cm, AC =14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.
(vi) If AD= 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AB= 3.6 cm, BC e 6 cm and BD = 32 cm, find AC.
(viii) If AB =10 cm, AC = 6 cm and BC = 12 cm, find BD and DC

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In ΔABC, B is a right angle and ¯¯¯¯¯¯¯¯¯BD is an altitude. If AB=8, and BC=6, find BD.

The correct option is B 4.8cmArea of ΔABC⇒12×(BC)(AC)=12×(AC)(BD)⇒(BC)(AB)=(AC)(BD) .........(1)ABC is right triangle AB2+BC2=AC2⇒82+62=AC2⇒AC=10 cm ......(2)Put (2) in (1)(6)×(8)=(10)(BD)BD=4.8 cm

In $Δ A B C$ , B is a right angle and $¯ ¯¯¯¯¯¯¯ ¯ B D$ is an altitude. If AB=8, and BC=6, find BD.