Question

Sides of a triangle are in the ratio of 2:7:5 and it's perimeter is 140cm finds it's area using heron's formula

Answer 1

Answer:

0 (triangle does not exist)

( In any triangle, the sum of the smaller sides have to be greater than the larger side. Here  20+50 = 70 , so triangles property is not satisfied. so the given triangle is actually a line)

Step-by-step explanation:

given the ratio of the sides of the triangle is 2:7:5

let x be the proportion

=> 2x+7x+5x = 140

=> 14x = 140

=> x = 10

ie, a = 2(10) = 20cm

    b = 7(10) = 70cm

    c = 5(10) = 50cm

By Herons formula,

Area of a triangle , A =  $\sqrt{s(s-a)(s-b)(s-c)}$

where s = half of perimeter

here s = 140/2 = 70

so Area , A = $\sqrt{70(70-20)(70-70)(70-50)}$

                  = 0

=> the triangle is actually a line.(3 vertices lying on the same line)

Answer 2

Answer:

0 (triangle does not exist)

( In any triangle, the sum of the smaller sides have to be greater than the larger side. Here  20+50 = 70 , so triangles property is not satisfied. so the given triangle is actually a line)

Step-by-step explanation:

given,

the ratio of the sides of the triangle is 2:7:5

let x be the proportion

=> 2x+7x+5x = 140

=> 14x = 140

=> x = 10

ie, a = 2(10) = 20cm

    b = 7(10) = 70cm

    c = 5(10) = 50cm

By Herons formula,

Area of a triangle , A =  \sqrt{s(s-a)(s-b)(s-c)}s(s−a)(s−b)(s−c)

where s = half of perimeter

here s = 140/2 = 70

so Area , A = \sqrt{70(70-20)(70-70)(70-50)}70(70−20)(70−70)(70−50)

                  = 0

=> the triangle is actually a line.(3 vertices lying on the same line)