Question

find the area of the triangle whose sides are 50cm,48cm and 14cm . find the height of the triangle corresponding to the side measuring 48cm I will mark brainiest whoever replies the correct ans with explanation​

Answer 1

$\Large \mathcal \orange {\dag ~~Question:-}$

Find the area of the triangle whose sides are 50cm, 48cm and 14cm. Find the height of the triangle corresponding to the side measuring 48cm.

$\Large \mathcal \orange {\dag~~Solution:-}$

The sides of the triangle are :-

• 50cm = a
• 48cm = b
• 14cm = c

Using Heron's formula to find the area :-

$\sf \red { \sqrt{s(s-a)(s-b)(s-c)} }$

Semi-perimeter (s) = $\sf \dfrac{a+b+c}{2}$

$\blue \mapsto \sf \cfrac{50cm+48cm+14cm}{2}$

$\blue \mapsto \sf Semi-perimeter (s) = 56cm$

Substituting and solving in the formula :-

$\green \mapsto \sf \sqrt{56(56-50)(56 - 48)(56 - 14)}$

$\green \mapsto \sf \sqrt{56(6)(8)(42)}$

$\green \mapsto \sf \sqrt{1,12,896}$

$\green \mapsto \sf 336cm^2$

✍️ Therefore, the are of the triangle with sides 50cm, 48cm and 14cm is $\sf 336cm^2$.

Height of the triangle corresponding to the side of 48cm can be given by :-$\sf \dfrac{1}{2}\times base\times height$

Here,

• Height = x
• Base = 48cm
• Area of the triangle = $\sf 336cm^2$

Substituting and solving :-

$\purple \mapsto \sf \cfrac{1}{2} \times( x) \times (48cm) = 336cm^2$

$\purple \mapsto \sf \dfrac{x}{\cancel 2} \times (\cancel{48}cm) = 336cm^2$

$\purple \mapsto \sf 24x=336cm^2$

$\purple \mapsto \sf x= \cfrac{336}{24}$

$\purple \mapsto \sf x=14cm$

✍️ Therefore, the height of the triangle corresponding to the side measuring 48cm is 14cm.

________________________

All done :)