The length of diagonal of a rhombus are 17.5 and 14.5 cm respectively. If the first diagonal is increased by 10%, by what percent must the other diagonal be decreased so as to maintain the same area

Questions : The length of diagonal of a rhombus are 17.5 and 14.5 cm respectively. If the first diagonal is increased by 10%, by what percent must the other diagonal be decreased so as to maintain the same area?

Answer:  

 

Alternative 

Shortcut Formula:

$$\text{Percentage Decrease} = \frac{\text{Increase in First Diagonal} \times 100}{\text{Increase in First Diagonal} + 100}$$

Given:

• First diagonal = 17.5 cm, increased by 10%

• Second diagonal = 14.5 cm

• Area of a rhombus = $\frac{1}{2} \times d_1 \times d_2$

• New first diagonal = $17.5 + 10\%$ of 17.5

  $$= 17.5 + \frac{10}{100} \times 17.5 = 17.5 + 1.75 = 19.25 \text{ cm}$$

• Let the new second diagonal be $x$ cm.

• The area must remain the same.

Applying the formula:

$$\text{Percentage Decrease} = \frac{10 \times 100}{10 + 100}$$ $$= \frac{1000}{110} \approx 9.09\%$$

Final Answer:

The second diagonal must be decreased by approximately 9.09%.

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