Question

48 ,70 sides of a triangle ,perimeter is 154 ,find area

Answer 1

Answer :

Given Sides of Triangle = 48 cm, 70 cm

Let the third side be x

Given Perimeter = 154

As we know that Perimeter of Triangle = Sum of the sides.

Therefore --


=> 48 + 70 + x = 154

=> add the numbers

=> 118 + x = 154

=> collect like terms

=> x = 154 - 118

=> subtract the numbers

=> x = 36


Therefore third side of Triangle = 36 cm

Let a = 48 cm

b = 70 cm

c = 36 cm


Area of Triangle can be found by Hero's formula

which is ---


$= > \: \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = > \: where \: s \: is \: semiperimeter \\ \\ = > \: a \: \: b \: \: and \: c \: are \: sides \: of \: triangle \\ \\ = > \: semiperimeter \: (s) \: = \: \frac{perimeter}{2} \\ \\ = > \: s \: = \: \frac{154}{2} \\ \\ = > \: s = \: 77 \: cm \: \\ \\ now \: area \: = \: \\ \\ \sqrt{77(77 - 48)(77 - 70)(77 - 36)} \\ \\ = > \: \sqrt{77 \times 29 \times 7 \times 41} \\ \\ = > \sqrt{640871} \\ \\ = > \: \sqrt{ {7}^{2} \times 13079} \\ \\ = > \: \sqrt{ {7}^{2} } \sqrt{13079} \\ \\ = > \: 7 \sqrt{13079} \\ \\ = > \: 800.54419 \: {cm}^{2} \\ \\ or \: \: \: \: \: 8.00544 \: m {}^{2}$


Hope it would help you