Question

One side other than the hypotenuse of a right-angled isosceles triangle is $4$ cm. The length of the perpendicular on the hypotenuse from the opposite vertex is:

• A. $8$cm
• B. $4\sqrt{2}$cm
• C. $4$ cm
• D. $2\sqrt{2}$cm

Answer 1

Answer: (D)

$2\sqrt{2}$cm

Let assume A, B, C be the vertices of the given triangle and right-angled at A i.e, $\angle A={90}^{\circ }$, $AD\perp BC$.......(D is the point of intersecton of perpendicular from A on BC)

By Pythagoras theorem,
$B{C}^2=A{B}^2+A{C}^2$
$B{C}^2=4^2+4^2$
$BC=4\sqrt{2}$ cm
Area of triangle = $\frac{1}{2}base\times height$
Thus, $\frac{1}{2}AB\times AC=\frac{1}{2}AD\times BC$
$4\times 4=4\sqrt{2}\times AD$
$AD=2\sqrt{2}$ cm