Question

The ratio of the base and height of a rectangle is 3 to 8. The perimeter of the rectangle is 138.6 cm.

Write and solve an equation to find the length of the base and height.


1.What is the length of the base?

2.What is the length of the height?

3.Calculate the area of the rectangle.

Answer 1

1. The length of the base of the rectangle is 18.9 cm.

2. The height of the rectangle is 50.4 cm.

3. The rectangle's area is 952.56 cm².

Explanation:

Given:

The ratio of the base and height of a rectangle is 3 to 8.

And its perimeter is 138.6 cm.

Now, to write and solve an equation to find the length of the base and height.

Let the length of the base be
`3x.`

And let the length of the height be
`8x.`

Perimeter of rectangle = 138.6 cm.

Now, we put equation to get the base and height by putting formula of perimeter:

`Perimeter=2* base+2* height`

`138.6=2* 3x+2* 8x`

`138.6=6x+16x\\\\138.6=22x`

Dividing both sides by 22 we get:

`6.3=x\\\\x=6.3.`

Substituting the value of
`x`:

Base =
`3x`

=
`3* 6.3=18.9\ cm.`

Height =
`8x`

=
`8* 6.3=50.4\ cm.`

Now, to get the area of the rectangle by putting formula:

`Area=base* height\\\\Area=18.9* 50.4\\\\Area=952.56\ cm^2.`

Therefore, 1. the length of the base of the rectangle is 18.9 cm.

2. The height of the rectangle is 50.4 cm.

3. The rectangle's area is 952.56 cm².