Question
The length of one diagonal of a rhombus is 8 cm. The area of the rhombus is 72 square centimeters. What is the length of the other diagonal of the rhombus?
Answers
GPT-4o mini
The area \( A \) of a rhombus can be calculated using the lengths of its diagonals \( d_1 \) and \( d_2 \) with the formula:
\[
A = \frac{1}{2} d_1 d_2
\]
In this problem, we are given that one diagonal \( d_1 \) is 8 cm, and the area \( A \) is 72 square centimeters. We need to find the length of the other diagonal \( d_2 \).
Substituting the known values into the area formula, we have:
\[
72 = \frac{1}{2} (8) d_2
\]
To isolate \( d_2 \), we can first multiply both sides of the equation by 2 to eliminate the fraction:
\[
144 = 8 d_2
\]
Next, we divide both sides by 8:
\[
d_2 = \frac{144}{8} = 18
\]
Thus, the length of the other diagonal \( d_2 \) is:
\[
\boxed{18} \text{ cm}
\]
\[
A = \frac{1}{2} d_1 d_2
\]
In this problem, we are given that one diagonal \( d_1 \) is 8 cm, and the area \( A \) is 72 square centimeters. We need to find the length of the other diagonal \( d_2 \).
Substituting the known values into the area formula, we have:
\[
72 = \frac{1}{2} (8) d_2
\]
To isolate \( d_2 \), we can first multiply both sides of the equation by 2 to eliminate the fraction:
\[
144 = 8 d_2
\]
Next, we divide both sides by 8:
\[
d_2 = \frac{144}{8} = 18
\]
Thus, the length of the other diagonal \( d_2 \) is:
\[
\boxed{18} \text{ cm}
\]