One diagonal of a kite is four times as long as the other diagonal. If the area of the kite is 72 square meters, what are the lengths of the diagonals?Multiple choice question.A)8 m; 16 mB)6 m; 24 mC)8 m; 14 mD)7 m; 13 m

To solve this problem, we need to use the formula for the area of a kite. The area $A$ of a kite can be calculated using the lengths of its diagonals $d_1$ and $d_2$:

$A = \frac{1}{2} \times d_1 \times d_2$

We are given that one diagonal is four times as long as the other diagonal. Let's denote the shorter diagonal as $d_1$ and the longer diagonal as $d_2$. According to the problem:

$d_2 = 4 \times d_1$

We are also given that the area of the kite is 72 square meters. Substituting the given values into the area formula, we get:

$72 = \frac{1}{2} \times d_1 \times d_2$

Substitute $d_2 = 4 \times d_1$ into the equation:

$72 = \frac{1}{2} \times d_1 \times (4 \times d_1)$

Simplify the equation:

$72 = \frac{1}{2} \times 4 \times d_1^2$

$72 = 2 \times d_1^2$

Divide both sides by 2:

$36 = d_1^2$

Take the square root of both sides:

$d_1 = 6$

Now, substitute $d_1 = 6$ back into the equation for $d_2$:

$d_2 = 4 \times d_1$

$d_2 = 4 \times 6$

$d_2 = 24$

So, the lengths of the diagonals are 6 meters and 24 meters. The correct answer is:

B) 6 m; 24 m