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3 years ago

the area of a square can be quadrupled by increasing the side length and width by 4 inches. what is the side length?

Mathematics

2 answers:

vodomira [7]3 years ago

7 0

The number could be anything because whatever it is it can be quadrupled

Elenna [48]3 years ago

5 0

Let the original side of the square be x inches.When sides are increased by 4 inches the sides are x+4 inches.

Area of square with side x inches= $x^{2}.$

Area of square with sides x+ inches= $(x+4)^{2}.$

According to question:The area of a square can be quadrupled by increasing the side length and width by 4 inches.\

Or $4x^{2}=(x+4)^{2}$

Expanding we have:

$4x^{2}=x^{2}+8x+16.$

Or, $3x^{2}-8x-16=0.$

Factoring,

(3x+4)(x-4)=0

3x+4=0 or x=4

x= $-\frac{4}{3}.$ Or x=4.

Sides can not be negative so x=4.

The sides of the square will be 4 inches.

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mariarad [96]

ANSWER

49:16

EXPLANATION

If the similarity ratio is

7:4

Then, the scale factor is

$k= \frac{7}{4}$

The scale factor for the area is

${k}^{2} = \frac{ {7}^{2} }{ {4}^{2} }$

${k}^{2} = \frac{49}{16}$

Therefore the ratio of their areas is:

49:16

7 0

3 years ago

In a survey of 3450 registered voters who reside in California, 1789 were

morpeh [17]

Subtraction. both numvers

7 0

3 years ago

Draw a isosceles triangle ABC in which AB=AC=6cm and BC=5cm. Construct a triangle PQR similar to triangle ABC in which PQ=8cm. A

xenn [34]

Answer:

See the diagram

Step-by-step explanation:

$ABC \cong PQR\\\Rightarrow \frac{PQ}{AB} =\frac{PR}{AC}=\frac{QR}{BC} \\\frac{PQ}{AB}=\frac{PR}{AC}\\ \\Since \ AB=AC\\PQ=PR\\PR=8cm\\\\\frac{PQ}{AB}=\frac{QR}{BC}\\\\QR=\frac{PQ}{AB} \cdot BC\\\\QR=\frac{8}{6} \cdot 5\\\\QR=\frac{20}{3}$

5 0

3 years ago

Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the job alone she can finish it in 5 hours. If Paul

rusak2 [61]

<h3>Answer: 7.5 hours (or 7 hours 30 minutes)</h3>

==================================================

Explanation:

Jane does the job alone and she can finish it in 5 hours. Her rate is 1/5 of a job per hour. By "job", I mean painting the entire fence. Notice that multiplying 1/5 by the number of hours she works will yield the value 1 to indicate one full job is done.

Through similar reasoning, Paul's rate is 1/6 of a job per hour.

Let x be the time, in hours, it takes Peter to get the job done if he worked alone. His rate is 1/x of a job per hour.

Combining the three individual rates gives

1/5 + 1/6 + 1/x = (6x)/(30x) + (5x)/(30x) + (30)/(30x)

1/5 + 1/6 + 1/x = (6x+5x+30)/(30x)

1/5 + 1/6 + 1/x = (11x+30)/(30x)

The expression (11x+30)/(30x) is the total rate if the three people worked together. This is assuming neither worker slows another person down.

Set this equal to 1/2 as this is the combined rate (based on the fact everyone teaming up gets the job done in 2 hours). Then solve for x

(11x+30)/(30x) = 1/2

2(11x+30) = 30x*1 .... cross multiply

22x+60 = 30x

60 = 30x-22x

60 = 8x

8x = 60

x = 60/8

x = 7.5

It takes Peter 7.5 hours, or 7 hours 30 minutes, to get the job done if he worked alone.

--------------

Here's another equation to solve though its fairly the same idea as above

1/5 + 1/6 + 1/x = 1/2

30x*(1/5 + 1/6 + 1/x) = 30x*(1/2) ... multiply both sides by LCD

30x(1/5) + 30x(1/6) + 30x(1/x) = 30x(1/2)

6x + 5x + 30 = 15x

11x + 30 = 15x

30 = 15x-11x

30 = 4x

4x = 30

x = 30/4

x = 7.5

We get the same answer

5 0

3 years ago

Read 2 more answers

A school orchestra has 60 member. 20% of the members are percussionists. How many orchestra members are percussionists?

mafiozo [28]

Out of 60
Members 20% are percussionsists or 1/5 divide 60 by 5 or multiply 60 by 0.2 and you will get the answer. The answer is 12.

6 0

2 years ago