Mathematics, 10.10.2019 20:30 majj979

Written assignment
the perimeter of a rectangle must be greater than 70 cm, but the length cannot be greater than 30 cm and the width cannot be greater than 20 cm. represent the length with x and the width with y
a) write 3 constraints (inequalities) for this problem
b) graph all 3 constraints (edit the image or tell me where to plot)
c) what are two possible combinations for the length and width of the rectangle

Answers: 3

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Answer from: kingteron6166

Part a)

(x+y) 35

$x \leq 30$

$y \leq 20$

Part b) The graph in the attached figure

Part c) (30,20) and (25,15)

Step-by-step explanation:

Part a) write 3 constraints (inequalities) for this problem

Let

x -----> the length of the rectangle

y -----> the width of the rectangle

we know that

The perimeter of rectangle is

P=2(x+y)

$P 70\ cm$

2(x+y) 70 ---> the perimeter of a rectangle must be greater than 70 cm

Simplify

(x+y) 35 ----> inequality A

$x \leq 30$ ----> inequality B (the length cannot be greater than 30 cm)

$y \leq 20$ ----> inequality C (the width cannot be greater than 20 cm)

Part b) Graph all 3 constraints

we have

(x+y) 35

$x \leq 30$

$y \leq 20$

using a graphing tool

The solution is the triangular shaded area

see the attached figure

Part c) what are two possible combinations for the length and width of the rectangle

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy all the inequalities of the system (The ordered pair must lie on the shaded area of the graph)

First possible combination

point (30,20) ----> the point lie on the shaded area

x=30 cm, y=20 cm

Verify if the ordered pair satisfy the inequalities

Inequality A

(x+y) 35

(30+20) 35

(50) 35 ----> is true

The ordered pair satisfy the inequality A

Inequality B

$x \leq 30$

$30 \leq 30$ ---> is true

The ordered pair satisfy the inequality B

Inequality C

$y \leq 20$

$20 \leq 20$ ----> is true

The ordered pair satisfy the inequality C

The ordered pair satisfy all the inequalities of the system

therefore

The ordered pair (30,20) is a possible combinations for the length and width of the rectangle

Second possible combination

point (25,15) ----> the point lie on the shaded area

x=25 cm, y=15 cm

Verify if the ordered pair satisfy the inequalities

Inequality A

(x+y) 35

(25+15) 35

(40) 35 ----> is true

The ordered pair satisfy the inequality A

Inequality B

$x \leq 30$

$25 \leq 30$ ---> is true

The ordered pair satisfy the inequality B

Inequality C

$y \leq 20$

$15 \leq 20$ ----> is true

The ordered pair satisfy the inequality C

The ordered pair satisfy all the inequalities of the system

therefore

The ordered pair (25,15) is a possible combinations for the length and width of the rectangle

Written assignment the perimeter of a rectangle must be greater than 70 cm, but the length cannot b

Answer from: Quest

is this part of a question or something

Answer from: Quest

Patrick earns the most money per hour

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