Question

$\Delta ABC$is an isosceles right angled triangle and BD $\perp$ AC, DC = 5. Find x.

• A. 10
• B. 5√2
• C. 5
• D. 10√2

Answer 1

The correct option is C

5

$\Delta$BDC $\cong$ $\Delta$ADB (1 right angle and two equal sides) AD = CD = 5 $\therefore$From $\Delta$ADB -- BD${}^2$ = AB${}^2$- AD${}^2$ $\Rightarrow$ BD${}^2$= $\frac{(5+5{)}^2}{2}$ - 5${}^2$ $\Rightarrow$ BD = x = 5.