Question

A plant that manufactures metal plates has a quality control team to check that the plates are the right size. A rectangular plate with dimensions 5 cm by 3 cm must have a length within 0.25 cm of 5 cm. Write and solve an absolute value inequality to find the minimum and maximum area of the plates. (Round to the nearest hundredth)

a) Minimum: 12.00 cm²
b) Minimum: 11.25 cm²
c) Maximum: 15.00 cm²
d) Maximum: 15.25 cm²

Answer 1

To find the minimum and maximum area of the plates, we use the given dimensions and the range for the length. The minimum area is 14.25 cm² and the maximum area is 15.75 cm².

Step-by-step explanation:

To find the minimum and maximum area of the plates, we can use the given dimensions and the range for the length. The length of the plate should be within 0.25 cm of 5 cm. Let's start by defining the length of the plate, which we'll call 'l'.

The inequality for the length can be written as |l - 5| ≤ 0.25 cm. We can solve this inequality by breaking it into two separate inequalities.

For the first inequality, we have l - 5 ≤ 0.25 cm. Solving for l, we get l ≤ 5.25 cm.

For the second inequality, we have l - 5 ≥ -0.25 cm. Solving for l, we get l ≥ 4.75 cm.

Now we can find the minimum and maximum area by multiplying the length and breadth. The minimum area is 3 cm * 4.75 cm = 14.25 cm², rounded to the nearest hundredth. The maximum area is 3 cm * 5.25 cm = 15.75 cm², rounded to the nearest hundredth.