Question

what is the value of m in the figure below? in this diagram, △abd ~ △bcd.

Explanation:

Step1: Use property of similar triangles

Since $\triangle ABD\sim\triangle BCD$, the ratios of corresponding sides are equal. That is $\frac{BD}{CD}=\frac{AD}{BD}$. Cross - multiplying gives $BD^{2}=AD\times CD$. Here $AD = 11$ and $CD=7$, so $BD^{2}=11\times7 = 77$.

Step2: Apply Pythagorean theorem in $\triangle BCD$

In right - triangle $\triangle BCD$, by the Pythagorean theorem $BC^{2}=BD^{2}+CD^{2}$. We know $BD^{2}=77$ and $CD = 7$, so $m^{2}=77+49=126$. Then $m=\sqrt{126}$.

Answer:

A. $\sqrt{126}$