Question

The rectangle shown has a length of 4x+3 and a width of 3x. Show your work. (3 points) Find the perimeter. Find the area. Find the perimeter and area if x = 8. *URGENT 20 POINTS*

Answer 1

We have been given that the rectangle has a length of
`4x+3` and width of
`3x`. We are asked to find the area and perimeter of the rectangle, when
`x=8`.

We know that perimeter of rectangle is 2 times sum of length and width.

`\text{Perimeter}=2* (\text{Length}+\text{Width})`

`\text{Perimeter}=2* (4x+3+3x)`

`\text{Perimeter}=2* (7x+3)`

`\text{Perimeter}=2* (7(8)+3)`

`\text{Perimeter}=2* (56+3)`

`\text{Perimeter}=2* (59)`

`\text{Perimeter}=118`

Therefore, the perimeter of the rectangle is 118 units.

We know that area of rectangle is width times length.

`\text{Area}=\text{Length}* \text{Width}`

`\text{Area}=(4x+3)* 3x`

`\text{Area}=12x^2+9x`

`\text{Area}=12(8)^2+9(8)`

`\text{Area}=12(64)+72`

`\text{Area}=768+72`

`\text{Area}=840`

Therefore, the area of the rectangle is 840 square units.