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Masja [62]
3 years ago
14

Give the dimensions of the rectangle with an area of 100 square units and whole number side lengths that has the largest perimet

er and the smallest perimeter?
Mathematics
1 answer:
attashe74 [19]3 years ago
8 0
25 and 4=100. length times width. 
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Pls solve the simultaneous equation in the attachment.
siniylev [52]

Answer:

Part a) The solution is the ordered pair (6,10)

Part b) The solutions are the ordered pairs (7,3) and (15,1.4)

Step-by-step explanation:

Part a) we have

\frac{x}{2}-\frac{y}{5}=1 ----> equation A

y-\frac{x}{3}=8 ----> equation B

Multiply equation A by 10 both sides to remove the fractions

5x-2y=10 ----> equation C

isolate the variable y in equation B

y=\frac{x}{3}+8 ----> equation D

we have the system of equations

5x-2y=10 ----> equation C

y=\frac{x}{3}+8 ----> equation D

Solve the system by substitution

substitute equation D in equation C

5x-2(\frac{x}{3}+8)=10

solve for x

5x-\frac{2x}{3}-16=10

Multiply by 3 both sides

15x-2x-48=30

15x-2x=48+30

Combine like terms

13x=78

x=6

<em>Find the value of y</em>

y=\frac{x}{3}+8

y=\frac{6}{3}+8

y=10

The solution is the ordered pair (6,10)

Part b) we have

xy=21 ---> equation A

x+5y=22 ----> equation B

isolate the variable x in the equation B

x=22-5y ----> equation C

substitute equation C in equation A

(22-5y)y=21

solve for y

22y-5y^2=21

5y^2-22y+21=0

Solve the quadratic equation by graphing

The solutions are y=1.4, y=3

see the attached figure

<em>Find the values of x</em>

For y=1.4

x=22-5(1.4)=15

For y=3

x=22-5(3)=7

therefore

The solutions are the ordered pairs (7,3) and (15,1.4)

3 0
3 years ago
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