Question

Two sides of a triangle are 48cm and 70cm.If
perimeter is 154cm,
Find its area.
(class 9th)​

Answer 1

Given:

• 2 sides = 48 cm, 70 cm
• Perimeter = 154 cm

To find:

Area of triangle = ?

Solution:

$\sf{s = \dfrac{a + b+ c}{2}}\\\\\\\sf{where,}\\\\\star \sf{s = Semiperimeter}\\\\\star \sf{a, b, c \: are \: 3 \: sides}$

$\sf{\dfrac{154}{2} = \dfrac{48 + 70 + c}{2}}\\\\\\\rightarrow \: \sf{154 = 118 + c}\\\\\rightarrow \: \sf{c = 154 - 118}\\\\\rightarrow \: \sf{c = 36 \: cm}$

So, the third side = 36 cm

By Heron's formula,

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

$\Rightarrow \sf{Area = \sqrt{77(77-48)(77-70)(77-36)}}$

$\Rightarrow \: \sf{Area = \sqrt{77(29)(7)(41)}}$

$\Rightarrow \: \sf{Area = \sqrt{640871}}\\\\\\\therefore \boxed{\boxed{\bf{Area=800.5 \:cm^{2} }}}$