Question

find the measure of xy. answer attempt 1 out of 2

Explanation:

Step1: Apply Pythagorean theorem

In right - triangle $WXY$, if $WY = 40$ is the hypotenuse and $WX = 25$, and we want to find $XY$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a,b$ are the legs of the right - triangle. Let $XY=x$, $WX = 25$, and $WY = 40$. Then $x^{2}+25^{2}=40^{2}$.

Step2: Rearrange the equation

We can rewrite the equation as $x^{2}=40^{2}-25^{2}$. Calculate $40^{2}=1600$ and $25^{2}=625$. So $x^{2}=1600 - 625$.

Step3: Calculate the value of $x^{2}$

$1600−625 = 975$, so $x^{2}=975$.

Step4: Solve for $x$

Take the square root of both sides. $x=\sqrt{975}\approx31.22$.

Answer:

$\sqrt{975}$ or approximately $31.22$