Question

21. The width of a rectangle is four less than one half the length. If the perimeter of the rectangle is 94

meters, find the area of the rectangle.

Answer 1

442 square meters

Explanation:

Let the length of the rectangle be
`x` meters.

The width of a rectangle is four less than one half the length.

One half the length is
`(1)/(2) x`

four less than one half the length is
`(1)/(2) x - 4`

So, the width of the rectangle is
`(1)/(2) x - 4` meters.

Perimeter of a rectangle is
`2( \text{length} + \text{width})`.

The perimeter of the rectangle is 94 meters.

So,

`2(x+(1)/(2) x-4)=94`

`x + (1)/(2) x-4 = 47`

`x+(1)/(2) x=51`

`(3)/(2) x = 51`

`x = 51*(2)/(3)`

`x = 17*2`

`x = 34`

Hence, the length of the rectangle is 34 meters.

So, width is
`((1)/(2) * 34 - 4) = 13` meters.

Now, the area of a rectangle is
`\text{length} * \text{width}`

`= 34 * 13 = 442` square meters.

Answer 2

Good morning ☕️

______

Answer:

Area=13×34=442

___________________

Explanation:

w is the width

p is the perimeter

L is the length

w = L/2 - 4

p=2L+2w

⇔94=2L+2(L/2 - 4)

⇔94=2L+2L-8

⇔102=4L

⇔102/4 = L

⇔ L=34

w = L/2 - 4 = 34/2 - 4 = 17-4 = 13

Area=L×w=34×13=442.

:)