Question

quadrilateral jklm is a kite with an area of 63 square feet. what is the length of $overline{nm}$? (not drawn to scale) a 6 ft b 9 ft c 5 ft d 7 ft

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. In kite $JKLM$, one diagonal $JL = 7 + 7=14$ ft, and let the other diagonal be $KM=3 + NM$.

Step2: Substitute into the area formula

We know that $A = 63$ square - feet and $d_1=14$ ft. Substituting into $A=\frac{1}{2}d_1d_2$, we get $63=\frac{1}{2}\times14\times(3 + NM)$.

Step3: Simplify the equation

First, simplify the left - hand side of the equation: $\frac{1}{2}\times14 = 7$. So the equation becomes $63=7\times(3 + NM)$.

Step4: Solve for $NM$

Divide both sides of the equation by 7: $\frac{63}{7}=3 + NM$. Since $\frac{63}{7}=9$, we have $9 = 3+NM$. Then subtract 3 from both sides: $NM=9 - 3$.

Answer:

A. 6 ft