Question

quadrilateral abcd is a kite with an area of 80 square inches. the length of $overline{be}$ is 6 inches. what is the length of $overline{ed}$? (not drawn to scale) a 8 in. b 11 in. c 10 in. d 16 in.

Explanation:

Step1: Recall kite - area formula

The area formula of a kite is $A=\frac{1}{2}d_1d_2$, where $d_1$ and $d_2$ are the lengths of the diagonals. In kite $ABCD$, let $AC = d_1$ and $BD=d_2$. Given $AC=AE + EC=5 + 5=10$ inches and $BD=BE + ED$, and $A = 80$ square inches, $BE = 6$ inches.

Step2: Substitute values into the formula

We know that $A=\frac{1}{2}d_1d_2$. Substituting $A = 80$, $d_1=10$ into the formula, we get $80=\frac{1}{2}\times10\times d_2$.

Step3: Solve for $d_2$

First, simplify the right - hand side of the equation: $\frac{1}{2}\times10\times d_2 = 5d_2$. Then, solve the equation $80 = 5d_2$ for $d_2$. Divide both sides by 5: $d_2=\frac{80}{5}=16$ inches.

Step4: Find the length of $ED$

Since $d_2=BD=BE + ED$ and $BE = 6$ inches, then $ED=d_2 - BE$. Substitute $d_2 = 16$ and $BE = 6$ into the equation: $ED=16 - 6=10$ inches.

Answer:

C. 10 in.