Question

Use heron's formula to find the area of the triangle 7m and perimeter 70m

Answer 1

Answer

s=a+b+c/2

a=√(s-a)(s-b)(s-c)

Answer 2

Answer:

max area =  109.57 m²

76.68 m²

98.98 m²

108.44 m²

Step-by-step explanation:

Use heron's formula to find the area of the triangle 7m and perimeter 70m

One Side is given = 7 m

Perimeter = 70 m

Sum of other two sides = 70 - 7 = 63 m

Let say two other sides are a & b

a + b = 63 m

a - b < 7 m  ( as sum of two sides > third sides)

=> 2a < 70 m

=> a < 35 m

b > 28 m

so possible combination  of sides are

34 , 29 , 7  m

33  , 30 , 7  m

32 , 31 , 7    m

Case 1 - 34 , 29 , 7  

S = (34 + 29 + 7)/2 = 35 m

Hero formula for Area = $\sqrt{(s)(s-a)(s-b)(s-c)}$

Area = $\sqrt{(35)(35-34)(35-29)(35-7)}$

= $\sqrt{(35) (1)(6)(28)}$

= √5880

= 76.68 m²

Case 2 - 33 , 30 , 7  m

s = 35 m

Area = √(35)(2)(5)(28)

Area = √9800

Area = 98.98 m²

Case 3 - 32 , 31 , 7  m

s = 35 m

Area = √(35)(3)(4)(28)

Area = √11760

Area = 108.44 m²

Another possibility : if we say maximum area of trinagle

Then Triangle would be isosceles

remaining two sides are

(70-7)/2 = 31.5 m

s = 35 m

Area = √(35)(3.5)(3.5)(28)

= 109.57 m²