The area of a rectangular desk telephone is 868 square centimeters. The length is 3 centimeters longer than the width. We need to find the length and width in centimeters and then in millimeters.

1. Problem Description

The area of a rectangular desk telephone is 868 square centimeters. The length is 3 centimeters longer than the width. We need to find the length and width in centimeters and then in millimeters.

2. Solution Steps

(a) Let $w$ be the width of the desk telephone in centimeters and $l$ be the length in centimeters. We are given that the length is 3 centimeters longer than the width, so $l = w + 3$. We are also given that the area is 868 square centimeters, so $l \times w = 868$. Substituting $l = w + 3$, we have:

$(w + 3)w = 868$

$w^2 + 3w = 868$

$w^2 + 3w - 868 = 0$

We can solve this quadratic equation for $w$. We are given in the problem that the width is 28 centimeters, so we can verify this by plugging $w = 28$ into the quadratic equation:

$28^2 + 3(28) - 868 = 784 + 84 - 868 = 868 - 868 = 0$.

Thus, the width $w = 28$ centimeters.

Now we find the length $l = w + 3 = 28 + 3 = 31$ centimeters.

The area is $28 \times 31 = 868$ square centimeters, which confirms our solution.

(b) Now we convert the width to millimeters. We know that 1 centimeter is equal to 10 millimeters. Thus, to convert centimeters to millimeters, we multiply by

1

0. Width in millimeters = width in centimeters $\times$ 10

Width in millimeters = $28 \times 10 = 280$ millimeters

The length in millimeters is $31 \times 10 = 310$ millimeters.

3. Final Answer

The width of the rectangular desk telephone is 280 millimeters.