Question

in the figure, square wxyz has a diagonal of 12 units. point a is a midpoint of segment wx, segment ab is perpendicular to segment ac and ab=ac. what is the length of segment bc?

Answer 1

Answer: BC= 18 units .

Explanation:

Since we have given that

Diagonal of square WXYZ is given by

$12\sqrt{2}$

As we know the  formula of "Diagonal of square",

$D=a\sqrt2\\\\12=a\sqrt{2}\\\\\frac{12}{\sqrt{2}}=a\\\\6\sqrt{2}=a$

Since 'A' is the midpoint of WX so,

Length of AX=YE is given by

$\frac{6\sqrt{2}}{2}=3\sqrt{2}$

Since AB=AC and ΔABC is right angled triangle , so,

$\angle C=\angle B=45\textdegree(\text{ because equal sides have equal angles })$

So, In ΔCEY,

$\sin{45\textdegree}=\frac{EY}{CY}\\\\\frac{1}{\sqrt2}=\frac{3\sqrt2}{CY}\\\\CY=3\sqrt2\times \sqrt2=3\times 2=6\ units$

in ΔXYB,

$\sin{45\textdegree}=\frac{XY}{BY}\\\\\frac{1}{\sqrt2}=\frac{6\sqrt2}{CY}\\\\CY=6\sqrt2\times \sqrt2=6\times 2=12\ units$

So,

$BC=BY+CY\\\\BC=12+6\\\\BC=18\ units$