Question

In the given figure, AC = 10 cm and AB = 8 cm. A perpendicular is drawn from the midpoint of the hypotenuse of the right triangle to the base. Find the length of DE.

• A. 9 cm
• B. 8 cm
• C. 4 cm
• D. 3 cm

Answer 1

The correct option is D 3 cm

In $\Delta$ ABC, angle $B={90}^{\circ }$, by Pythagorean theorem,
$A{C}^2=A{B}^2+B{C}^2$
${10}^2=8^2+B{C}^2$
$B{C}^2=100-64=36$
$BC=\sqrt{36}=6$
In $\Delta$ ABC,
$\angle AED=\angle ABC={90}^{\circ }$
$ED||BC$
Also, D is the midpoint of AC, then
E is the midpoint of AB
Thus, $DE=\frac{BC}{2}$
$=\frac{1}{2}\times 6=3$ cm.