Question

In the figure given below, 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 = $\frac{1}{2}$ BC

= $\frac{1}{2}\times 6$ = 3 cm.