Question

In a $\Delta ABC,AB=AC=2.5cm,BC=4cm$. Find its height from $A$ to the opposite base.

• A. $1.5cm$
• B. $1cm$
• C. $2cm$
• D. $3cm$

Answer 1

The correct option is A $1.5cm$

$In△ABC$

In order to find height we need to consider that $AD\perp BC$

$Henceinrightangled△ADC$

${AC}^2={AD}^2+{DC}^2\left(PhythagoreasTheorm\right)$

$\Rightarrow {AD}^2={AC}^2-{DC}^2$

$\Rightarrow {AD}^2={\left(2.5\right)}^2-({2)}^2$

$\Rightarrow {AD}^2=6.25-4$

$\Rightarrow {AD}^2=2.25$

$\Rightarrow AD=1.5$

$Henceoption\left(A\right)isrightanswer$