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 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.

Step2: Identify the known diagonal length

One diagonal $JL = 7 + 7=14$ feet. Let the other diagonal be $KM=3 + NM$.

Step3: Substitute into the area formula

We know that $A = 63$ square - feet. Substituting into $A=\frac{1}{2}d_1d_2$, we have $63=\frac{1}{2}\times14\times(3 + NM)$.

Step4: Solve the equation for NM

First, simplify the left - hand side of the equation: $\frac{1}{2}\times14 = 7$. So the equation becomes $63=7\times(3 + NM)$.
Divide both sides by 7: $\frac{63}{7}=3 + NM$.
Since $\frac{63}{7}=9$, we have $9 = 3+NM$.
Subtract 3 from both sides: $NM=9 - 3=6$ feet.

Answer:

A. 6 ft