One of the sides of a parallelogram is 4.2 cm and the altitude to that side is 3.6 cm. Find the perimeter of the parallelogram if the altitude to the other side is 2.4 cm.

21 cm

21

21 see just because the world is flat doesn't mean it dumb.

21cmmmmm

21 cm

To find the perimeter of the parallelogram, we need to first find the length of the other side.

Given:
Side of the parallelogram: 4.2 cm
Altitude to that side: 3.6 cm
Altitude to the other side: 2.4 cm

In a parallelogram, the opposite sides are equal in length. So, the length of the other side is also 4.2 cm.

Now, let's find the length of the other base using the formula for the area of a parallelogram:

Area = base × height

We are given the base length (4.2 cm) and the corresponding altitude (3.6 cm), so we can substitute these values into the formula:

Area = 4.2 cm × 3.6 cm = 15.12 cm²

The area of a parallelogram can also be calculated as the product of any side length and the corresponding altitude. So, we can use the length of the other base (4.2 cm) and the given altitude (2.4 cm) to calculate the area:

Area = 4.2 cm × 2.4 cm = 10.08 cm²

Since the area of the parallelogram is the same regardless of which side and altitude we use, we can equate the two expressions for the area:

15.12 cm² = 10.08 cm²

Solving for the length of the other base (4.2 cm):

4.2 cm = 15.12 cm² / 2.4 cm = 6.3 cm

Now we have the lengths of both bases. To calculate the perimeter, we add the lengths of all four sides:

Perimeter = 2 × (Length of one base + Length of the other base)
= 2 × (4.2 cm + 6.3 cm)
= 2 × 10.5 cm
= 21 cm

Therefore, the perimeter of the parallelogram is 21 cm.

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Either side can be considered a base. So, since area = base * height, the missing side x is found via

2.4x = 3.6*4.2

Now, the perimeter is 2(4.2+x)

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