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

Good morning ☕️

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Answer:

Area=13×34=442

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Step-by-step 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.

:)

Answer 2

Answer:

442 square meters

Step-by-step 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 $\frac{1}{2} x$

four less than one half the length is $\frac{1}{2} x - 4$

So, the width of the rectangle is $\frac{1}{2} x - 4$ meters.

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

The perimeter of the rectangle is 94 meters.

So,

$2(x+\frac{1}{2} x-4)=94$

$x + \frac{1}{2} x-4 = 47$

$x+\frac{1}{2} x=51$

$\frac{3}{2} x = 51$

$x = 51\times\frac{2}{3}$

$x = 17\times2$

$x = 34$

Hence, the length of the rectangle is 34 meters.

So, width is $(\frac{1}{2} \times 34 - 4) = 13$ meters.

Now, the area of a rectangle is $\text{length} \times \text{width}$

$= 34 \times 13 = 442$ square meters.