Question

quadrilateral jklm is a kite with an area of 63 square feet. what is the length of nm? (not drawn to scale)

Explanation:

Step1: Recall kite - area formula

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 the diagonals of the kite $JKLM$ be $d_1$ and $d_2$. Assume the length of one diagonal is $d_1 = 14$ (from the figure, if we consider the given part of the diagonal) and the area $A = 63$ square feet.

Step2: Substitute values into the formula

We have $A=\frac{1}{2}d_1d_2$. Substituting $A = 63$ and $d_1=14$ into the formula, we get $63=\frac{1}{2}\times14\times d_2$.

Step3: Solve for $d_2$

First, simplify the right - hand side of the equation: $\frac{1}{2}\times14\times d_2 = 7d_2$. So, the equation becomes $7d_2=63$. Divide both sides by 7: $d_2=\frac{63}{7}=9$. If we assume the part of the diagonal we are looking for is part of $d_2$ and considering the symmetry of the kite, if the whole diagonal $d_2 = 9$ and we know one part from the figure, and assume the length of $NM$ is what we need to find, and from the way the kite is set up with the given information, we can find the length of the relevant part of the diagonal. Let's assume the other diagonal is split into two equal parts by the first diagonal. If we assume the whole diagonal related to the part $NM$ is $d_2$ and we know the area and one diagonal part, we find that the length of $NM$ is 9 feet.

Answer:

9 ft