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Ratio and Proportion

If a,b,c an...

Question

If $a, b, c$ and $d$ are in proportion, then

a b = c d

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a d = b c

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a c = b d

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n o n e o f t h e s e

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Solution

The correct option is B $a d = b c$
$P r o p o r t i o n i s e q u a l i t y o f t w o r a t i o s .$

$T h e r a t i o o f 2 t o 3 i s s a m e a s t h e r a t i o o f 4 t o 6, i . e .$

$2 : 3 = 4 : 6$

$T h e r e f o r e, t h e t w o r a t i o s 2 : 3 a n d 4 : 6 a r e p r o p o r t i o n a t e a n d w r i t t e n a s :$

$2 : 3 :: 4 : 6 a n d r e a d a s$

$T h e r a t i o o f 2 t o 3 i s s a m e a s t h a t o f 4 t o 6.$

$I f 2 : 3 = 4 : 6, t h e n$

$2 \times 6 = 3 \times 4, i . e .12 = 12,$

$L e t t w o r a t i o s a : b a n d c : d b e p r o p o r t i o n a t e,$

$i . e . a : b :: c : d$

$I n t h e p r o p o r t i o n a : b :: c : d$

$P r o d u c t o f m e a n s = p r o d u c t o f e x t r e m e s .$

$I f a : b = c : d, t h e n$

$a \times d = b \times c$

Suggest Corrections

Similar questions

∠ B A C = 90^{\circ} a n d A D ⊥ B C

B D . C D = B C^{2}

A B . A C = B C^{2}

B D . C D = A D^{2}

A B . A C = A D^{2}

∠ B A C = 90^{\circ} a n d A D ⊥ B C

B D . C D = B C^{2}

A B . A C = B C^{2}

B D . C D = A D^{2}

A B . A C = A D^{2}

In a trapezium ABCD, if AB || CD then $(A C^{2} + B D^{2})$ = ?

(a) $B C^{2} + A D^{2} + 2 B C . A D$

(b) $A B^{2} + C D^{2} + 2 A B . C D$

(d) $B C^{2} + A D^{2} + 2 A B . C D$

A D

D

B C

∠ A

Δ A B C

b = A C, c = A B, m = C D

n = B D

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