The area of a rhombus is 240 cm² and one of the diagonals is 16 cm. Find the other diagonal

Question

Accepted Answer

To find the other diagonal of the rhombus, we can use the formula for the area of a rhombus, which is given by:

$$ \text{Area} = \frac{1}{2} \times d_1 \times d_2 $$

where $ d_1 $ and $ d_2 $ are the lengths of the diagonals. We are given that the area of the rhombus is 240 cm² and one of the diagonals, $ d_1 $, is 16 cm. We need to find the length of the other diagonal, $ d_2 $.

Substituting the known values into the formula, we have:

$$ 240 = \frac{1}{2} \times 16 \times d_2 $$

To solve for $ d_2 $, we first multiply both sides of the equation by 2 to eliminate the fraction:

$$ 480 = 16 \times d_2 $$

Next, divide both sides by 16 to solve for $ d_2 $:

$$ d_2 = \frac{480}{16} = 30 $$

Therefore, the length of the other diagonal is 30 cm, which corresponds to Option 2.

**Explanation for why each of the other options is incorrect:**

1. **Option 1 (20 cm):** If $ d_2 $ were 20 cm, the area would be calculated as:
   $$ \text{Area} = \frac{1}{2} \times 16 \times 20 = 160 \, \text{cm}^2 $$
   This does not match the given area of 240 cm², so Option 1 is incorrect.

2. **Option 3 (25 cm):** If $ d_2 $ were 25 cm, the area would be calculated as:
   $$ \text{Area} = \frac{1}{2} \times 16 \times 25 = 200 \, \text{cm}^2 $$
   This does not match the given area of 240 cm², so Option 3 is incorrect.

3. **Option 4 (15 cm):** If $ d_2 $ were 15 cm, the area would be calculated as:
   $$ \text{Area} = \frac{1}{2} \times 16 \times 15 = 120 \, \text{cm}^2 $$
   This does not match the given area of 240 cm², so Option 4 is incorrect.

In conclusion, the only option that satisfies the condition of the given area is Option 2, with $ d_2 = 30 $ cm.