Question

The sides of a triangle are $50cm,78cm$ and $112cm$. The smallest altitude is....

• A. $20cm$
• B. $30cm$
• C. $40cm$
• D. $50cm$
• E. $Noneofthese$

Answer 1

Answer: (B)

$30cm$

let $a=50cm$

$b=78cm$

$c=112$

$S=\frac{a+b+c}{2}=\frac{50+78+112}{2}=\frac{240}{2}=120$

area = $\sqrt{s(s-a)(s-b)(s-c)}$

=$\sqrt{120(120-50)(120-78)(120-112)}$

=$\sqrt{2822400}$

=$1680c{m}^2$

longest side = $120cm$

corresponding to this side as the base the altitude will be smallest

area = $\frac{1}{2}\times base\times altitude=1680$

=$\frac{1}{2}\times 112\times altitude=1680$

altitude = $30cm$