Question

quadrilateral stuv is a kite. what is rt? 48 80 rt =

Explanation:

Step1: Recall kite - property

In a kite, the diagonals are perpendicular and one diagonal is bisected by the other. Let the diagonals be $SU$ and $VT$ which intersect at $R$. Assume $SU$ bisects $VT$.

Step2: Use the Pythagorean theorem

In right - triangle $RUT$, if we know two sides of the right - triangle formed by the diagonals of the kite. Let the length of $RU = 48$ and $UT=80$. By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs of the right - triangle. In right - triangle $RUT$, we want to find $RT$. We know that $RT^{2}=UT^{2}-RU^{2}$.

Step3: Calculate $RT$

Substitute $RU = 48$ and $UT = 80$ into the formula $RT=\sqrt{UT^{2}-RU^{2}}=\sqrt{80^{2}-48^{2}}=\sqrt{(80 + 48)(80 - 48)}=\sqrt{128\times32}=\sqrt{4096}=64$.

Answer:

$64$