Question

the difference between semi perimeter of a triangle and its side are 6 cm , 12 cm and 18 cm respectively the area of the triangle will be​

Answer 1

Answer:

6+12+18/2= 18 (semi perimeter)

now usinf heron's formula

Step-by-step explanation:

HOPE IT HELPS YOU..

Answer 2

Hint:

• In this question we first assume its semi perimeter. Then all three sides will be computed as the difference between these and the semi perimeter. Further apply formula for semi perimeter to compute the semi perimeter value. Further apply Heron's formula to compute the area of the triangle.

Complete step-by-step answer

Let us suppose the semi perimeter of the given triangle ABC is “s”. Its three sides are of the lengths “a”, “b” and “c” , as shown in the diagram.

AS given that difference between semi perimeter and sides are 6 cm , 12 cm and 18 cm respectively.

Thus, in the triangle ABC , we have

s - a = 6

s-b = 12

s- c = 18

Thus three sides will be as follows,

Thus three sides will be as follows,a = s-6

b = s-12

and c = s-18

Since formula for semi perimeter is,

$\\ \\ s = \frac{a + b + c}{2}$

Now using Heron's formula we get area -

$\\ \\ \\ \\ \\ \\ Area = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \\ \\ = \sqrt{36 \times 6 \times 12 \times 18} \\ \\ \\ \\ = \sqrt{6 \times 6 \times 6 \times 6 \times2 \times 2 \times 3 \times 3 } \\ \\ \\ \\ = 6 \times 6 \times 2 \times 3 = 216 {cm}^{2}$

NOTE:

• This type of question is solved in a very limited method. The above method is a very good method to solve such questions in which there will be less chances of doubt and errors. Here we have used the area formula for triangles based on Heron’s method.