Question

4. length and breadth of a rectangle are directly proportional. if length increases from 6 cm to 21 cm and if breadth now is 14 cm, then what was the breadth before any change in length occurred?Â

Answer 1

l1 / l2 =b1 /b2
6/21 =b1/14
2/7 =b1/14
2×14=7×b1
b1=2×14/7
b1=2×2
b1=4cm is answer

Answer 2

Given that the length and the breadth are directly proportional

Define x:

Let the original breadth be x

We will use the similar length rule to solve for the missing breadth:

$\dfrac{\text{Length 1}}{\text{Breadth 1}} = \dfrac{\text{Length 2}}{\text{Breadth 2}}$

Plug in the know values:

$\dfrac{\text{6}}{\text{x}} = \dfrac{\text{21}}{\text{14}}$

Solve x:

$\dfrac{\text{6}}{\text{x}} = \dfrac{\text{21}}{\text{14}}$

Cross multiply:

$21x = 6 \times 14$

Combine like terms:

$21x = 84$

Divide both sides by 21:

$x = 4$

Answer: The original breadth was 4 cm