A penmeter of a rectangle
1820 m and the length is
find area of rectangle in terms
Of .

Ask by Garza Lawson. in Nigeria

Mar 24,2025

Question

A penmeter of a rectangle 1820 m and the length is $$ x \mathrm{~cm} $$ find area of rectangle in terms Of $$ x $$.

UpStudy AI · Accepted Answer

Given that the perimeter $$ P $$ of a rectangle is given by

$$
P = 2\,( \text{length} + \text{width} )
$$

and we know that the perimeter is $$ 1820 $$ meters. Converting this to centimeters (since $$ 1 $$ meter equals $$ 100 $$ centimeters):

$$
1820 \ \text{m} = 1820 \times 100 = 182000 \ \text{cm}
$$

Let the length be $$ x $$ cm and the width be $$ w $$ cm. Then, the perimeter is

$$
2(x + w) = 182000
$$

Dividing both sides by $$ 2 $$:

$$
x + w = 91000
$$

Solving for $$ w $$:

$$
w = 91000 - x
$$

The area $$ A $$ of the rectangle is

$$
A = \text{length} \times \text{width} = x \times w
$$

Substitute $$ w $$ into the area formula:

$$
A(x) = x \times (91000 - x) = 91000x - x^2
$$
The area of the rectangle in terms of $$ x $$ is $$ A(x) = 91000x - x^2 $$.

A penmeter of a rectangle
1820 m and the length is
find area of rectangle in terms
Of .