The three sides of a triangle measure 6 cm, 8 cm and 10 cm respectively. A rectangle equal in area to the triangle has a length of 8 cm. The perimeter of the rectangle is:a)11 cmb)22 cmc)16 cmd)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Accepted Answer

Answer

When 3 sides given area formula is
√s(s-a)(s-b)(s-c)
where s=(a+b+c)/2

Answer

Given:

The three sides of the triangle measure 6 cm, 8 cm, and 10 cm respectively.
The rectangle has a length of 8 cm, and its area is equal to the area of the triangle.

To Find:

The perimeter of the rectangle.

Solution:

To find the perimeter of the rectangle, we need to find its width, as the perimeter is the sum of all its sides.

Finding the Area of the Triangle:

The area of a triangle can be found using the formula:
Area = (base * height) / 2

We can use the sides of the triangle as the base and height, as the triangle is a right-angled triangle.
Therefore, the area of the triangle is:
Area = (6 * 8) / 2 = 24 cm²

Finding the Width of the Rectangle:

We know that the area of the rectangle is equal to the area of the triangle.
So, the area of the rectangle is also 24 cm².

To find the width of the rectangle, we can divide the area by the length:
Width = Area / Length = 24 / 8 = 3 cm

Finding the Perimeter of the Rectangle:

Now that we know the length and width of the rectangle, we can find its perimeter by adding all the sides together:
Perimeter = 2 * (Length + Width) = 2 * (8 + 3) = 2 * 11 = 22 cm

Therefore, the perimeter of the rectangle is 22 cm, which corresponds to option B.

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