+0

# help!

0
162
1

ABC has a right angle at B. AC = 60, AE = 52 and CD=39.

Find the length of DE.

Jun 23, 2020

#1
+25644
+3

ABC has a right angle at B. $$AC = 60$$, $$AE = 52$$ and $$CD=39$$.
Find the length of $$DE$$.

$$\text{Let AD=t } \\ \text{Let BD=w } \\ \text{Let BE=u } \\ \text{Let CE=v } \\ \text{Let DE=\color{red}x }$$

$$\begin{array}{|lrcll|} \hline (1): & 60^2 &=& (u+v)^2+(t+w)^2 \\ (2): & 52^2 &=& u^2+(t+w)^2 \\ (3): & 39^2 &=& (u+v)^2+w^2 \\ (4): & x^2 &=& u^2+w^2 \\ \hline (4)+(1)-(2)-(3): \\ &x^2+60^2-52^2-39^2 &=& u^2+w^2 \\ &&& +(u+v)^2+(t+w)^2 \\ &&& - \left(u^2+(t+w)^2\right) \\ &&& -\left((u+v)^2+w^2 \right) \\\\ &x^2+60^2-52^2-39^2 &=& u^2+w^2 \\ &&& +(u+v)^2+(t+w)^2 \\ &&& - u^2-(t+w)^2 \\ &&& -(u+v)^2-w^2 \\\\ &x^2+60^2-52^2-39^2 &=& 0 \\ &x^2 &=& 52^2+39^2-60^2 \\ &x^2 &=& 625 \\ &\mathbf{x} &=& \mathbf{25} \\ \hline \end{array}$$

The length of DE is $$\mathbf{25}$$

Jun 23, 2020
edited by heureka  Jun 23, 2020