In the figure given below- if BD -2-4 cm - AC -3-6 cm - PD -4 cm - PB -3-2 cm- and AC is parallel to BD- then the lengths of PA - PC will beA- 4-8 cm and 6 cm respectivelyB- 6-8 cm and 4 cm respectivelyC- 6 cm and 4-8 cm respectivelyD- 4 cm and 6-8 cm respectively

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Parallel Lines and Transversal

In the figure...

Question

In the figure given below, if BD = 2.4 cm, AC = 3.6 cm, PD = 4 cm, PB = 3.2 cm, and AC is parallel to BD, then the lengths of PA & PC will be

4.8 cm and 6 cm respectively

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6.8 cm and 4 cm respectively

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6 cm and 4.8 cm respectively

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4 cm and 6.8 cm respectively

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Solution

The correct option is A
4.8 cm and 6 cm respectively

In $Δ A P C & Δ B P D$

$∠ A P C = ∠ B P D$ (Vertically opposite angle)
$∠ A C P = ∠ B D P$ (Alternate angle)
$∴ Δ A P C \sim Δ B P D$ by AA similarity criterion.

$\frac{A P}{A C} = \frac{B P}{B D}$ (Ratio of corresponding sides of similar triangles)
$\frac{A P}{3.6} = \frac{3.2}{2.4}$
AP = 4.8 cm

Also, $\frac{P C}{A P} = \frac{P D}{B P} \frac{P C}{4.8} = \frac{4}{3.2}$
PC = 6 cm

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Similar questions

In the figure given below, if BD = 2.4 cm, AC = 3.6 cm, PD = 4 cm, PB = 3.2 cm, and AC is parallel to BD, then find the lengths of PA & PC.

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Construct a rhombus ABCD, if ;

(i) AB = 4 cm and $∠ B = 120^{\circ}$ .

(ii) BC = 4.7 cm and $∠ B = 75^{\circ}$

(iii) CD = 5 cm and diagonal BD = 8.5 cm.

(iv) BC = 4.8 cm, and diagonal AC = 7 cm.

(v) diagonal AC = 6 cm and diagonal BD = 5.8 cm.

(vi) diagonal AC = 4.9 cm and diagonal BD = 6 cm.

(vii) diagonal AC = 6.6 cm and diagonal BD = 5.3 cm.

In a $Δ A B C$ , AD is the bisector of $∠ A$ .

(i) If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC.

(ii) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.

(iii) If AB = 5.6 cm, BD = 3.2 cm and BC = 6 cm, find AC.

(iv) If AB = 5.6 cm, AC = 4 cm and DC = 3 cm, find BC.

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