Question

2. A triangle whose area and perimeter is equal are called super triangle . For example a triangle with sides 6, 8,10 is a super triangle.
Explore such triangles. ( Any 4)​

Answer 1

Answer:

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1) 5 , 12 ,13 side

2) 6 , 6 , 6 side

3) 7 , 6 , 8 side

4) 10 , 10 , 30 side

Step-by-step explanation:

Answer 2

All the right angles triangles are considered super triangles.

• Consider a triangle with sides a, b, and c. The perimeter of the triangle is defined as the sum of the lengths of the sides of the triangle divided by 2.

=> Perimeter of a triangle = (a+b+c)/2.

• Consider a triangle with its base side of length b and has a height of h units, the area of the triangle is given by the formula,

=> Area of the triangle = (0.5) x (base) x (height).

• Consider a right-angled triangle with the following cases:

1. Let the sides of the triangle be 3, 4, and 5. It is a right-angled triangle with 5 as its hypotenuse. The perimeter of this triangle is (12/2) = 6 units. The area of this triangle is 0.5 x 4 x 3 = 6 units. Both the area and perimeter are equal, hence it is considered as a super triangle.

2. Let the sides of the triangle be 6, 8, and 10. It is a right-angled triangle with 10 as its hypotenuse. The perimeter of this triangle is (24/2) = 12 units. The area of this triangle is 0.5 x 8 x 6 = 12 units. Both the area and perimeter are equal, hence it is considered as a super triangle.

3.  Let the sides of the triangle be 5, 12, and 13. It is a right-angled triangle with 5 as its hypotenuse. The perimeter of this triangle is (30/2) = 15 units. The area of this triangle is 0.5 x 5 x 12 = 30 units. Both the area and perimeter are equal, hence it is considered as a super triangle.

• From the above examples, it can be concluded that a right-angled triangle can be considered a super triangle.

Therefore, every right-angled triangle is a super triangle i.e, they have the same area and perimeter.