Question

figure abcd is a kite. the area of abcd is 48 square units. the length of line segment bd is 8 units. what is the length of ac? 10 units 12 units 5 units 6 units

Explanation:

Step1: Recall the area formula for a kite

The area formula for a kite is \( A=\frac{1}{2}d_1d_2 \), where \( d_1 \) and \( d_2 \) are the lengths of the diagonals. Let \( d_1 = BD\) and \( d_2=AC\). We know that \( A = 48\) and \( BD=8\).

Step2: Substitute the known values into the formula

Substitute \( A = 48\) and \( d_1=8\) into \( A=\frac{1}{2}d_1d_2\). We get \( 48=\frac{1}{2}\times8\times d_2\).

Step3: Solve for \( d_2\)

First, simplify the right - hand side of the equation: \(\frac{1}{2}\times8\times d_2 = 4d_2\). Then, solve the equation \( 48 = 4d_2\) for \( d_2\). Divide both sides by 4: \( d_2=\frac{48}{4}=12\).

Answer:

12 units