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A parallelogram has a height of x cm. The length of its base is 4 cm greater than its height. A triangle has the same height as the parallelogram. The length of the triangle’s base is 20cm.

What is the value when the triangle and the parallelogram have the same area?

Respuesta :

MrRoyal

The value of x when the triangle and the parallelogram have the same area is 6 units

The dimensions

The dimension of the parallelogram is given as:

  • Height = x
  • Base = 4 + x

The dimension of the triangle is given as:

  • Height = x
  • Base = 20

Areas

The area of a shape is the amount of space it occupies

The area of the parallelogram is calculated as:

[tex]Area = x (4 + x)[/tex]

The area of the triangle is calculated as:

[tex]Area = 0.5 \times 20 \times x[/tex]

[tex]Area = 10x[/tex]

Both areas are equal.

So, we have:

[tex]x(4 + x) = 10x[/tex]

Divide both sides by x

[tex]4 + x = 10[/tex]

Subtract 4 from both sides

[tex]x =6[/tex]

Hence, the value of x is 6 units

Read more about areas at:

https://brainly.com/question/2126265

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