Find the length of AD- if BD -3-6 cm and DC -6-4 cm-A- 5-2 cmB- 4-8 cmC- 3-8 cmD- 3-6 cm

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Standard X

Mathematics

Pythagoras Theorem

Find the leng...

Question

Find the length of AD, if BD= 3.6 cm and DC = 6.4 cm.

5.2 c m

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4.8 c m

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3.8 c m

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3.6 c m

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Solution

The correct option is B $4.8 c m$

Perpendicular from right angle to hypotenuse divides the triangle into two similar triangles and these are similar to the whole triangle also.

$∴ A D B \sim C D A$
$⟹ \frac{A D}{C D} = \frac{D B}{D A}$
${A D}^{2} = C D \times B D$
$= 6.4 \times 3.6$
$A D = 4.8 c m$

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and

E C = 6 c m

Δ P Q R \sim Δ L T R

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Construct

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, then the measure of LT is equal to ____ cm.

Q. In ∆ ABC, AB = 2.5 cm and BC = 6 cm. Then, the length of AC cannot be
(a) 3.4 cm
(b) 4 cm
(c) 3.8 cm
(d) 3.6 cm

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

Q. Construct a quadrilateral

A B C D

in which

A B = 3.6 c m, B C = 3.3 c m, A D = 2.7 c m

, diagonal

A C = 4.6 c m

and diagonal

B D = 4 c m

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Find the length of AD, if BD= 3.6 cm and DC = 6.4 cm.

The correct option is B 4.8 cm Perpendicular from right angle to hypotenuse divides the triangle into two similar triangles and these are similar to the whole triangle also. ∴ADB∼CDA ⟹ADCD=DBDA AD2=CD×BD =6.4×3.6 AD=4.8 cm