The area of a kite is 920 square meters. If one diagonal is three times the length of the other diagonal, what are the lengths of the diagonals? Round to the nearest tenth.Multiple choice question.A)23.3 in., 70.0 in.B)20.1 in., 60.3 in.C)31.2 in., 91.6 in.D)24.8 in., 74.3 in.

To solve this problem, we need to use the formula for the area of a kite, 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 kite is 920 square meters and that one diagonal is three times the length of the other diagonal. Let's denote the shorter diagonal as $d_1$ and the longer diagonal as $d_2$. According to the problem, $d_2 = 3d_1$.

Substitute $d_2$ in the area formula:

$920 = \frac{1}{2} \times d_1 \times 3d_1$

Simplify the equation:

$920 = \frac{1}{2} \times 3d_1^2$

$920 = \frac{3}{2} d_1^2$

Multiply both sides by 2 to clear the fraction:

$1840 = 3d_1^2$

Divide both sides by 3:

$d_1^2 = \frac{1840}{3}$

$d_1^2 = 613.33$

Take the square root of both sides to find $d_1$:

$d_1 = \sqrt{613.33}$

$d_1 \approx 24.8$

Since $d_2 = 3d_1$:

$d_2 = 3 \times 24.8$

$d_2 \approx 74.4$

So, the lengths of the diagonals are approximately 24.8 meters and 74.4 meters. The closest match to these values in the given options is:

D) 24.8 in., 74.3 in.