A plant that manufactures metal plates has a quality control team to check that the plates are the right size. A rectangular plate advertised as 5 cm by 3 cm must have a length within 0.25 cm of 5 cm. Use the solution to the equation |x − 5| − 0.25 = 0 to find the minimum and maximum area, in sq. cm, of the plates.

Question

10-09-2022
Mathematics

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A plant that manufactures metal plates has a quality control team to check that the plates are the right size. A rectangular plate advertised as 5 cm by 3 cm must have a length within 0.25 cm of 5 cm. Use the solution to the equation |x − 5| − 0.25 = 0 to find the minimum and maximum area, in sq. cm, of the plates.

Answer :

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ogorwyne ogorwyne · Answer 1 · 2022-09-13T18:29:01-04:00

The minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2

What is area of rectangle?

In mathematics, area of rectangle refers to the product of length of the rectangle and width of the rectangle. The unit is in square units. Area shows the extent a surface or a plane covers

Given data

size of rectangular plate = 5 cm by 3cm.

the length should be within = 0.25 of 5 cm

How to solve for the minimum and maximum area

This means the length, L of the rectangular plate can be mathematically represented as

5 - 0.25 ≤ L ≤ 5 + 0.25

4.75 ≤ L ≤ 5.25

Area of rectangle = Length × Width.

Width = 3

minimum length = 4.75

maximum length = 5.25

minimum length

= 4.75 * 3

= 14.25 cm^2

maximum length

= 5.25 * 3

= 15.75 cm^2

Therefore, the minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2

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