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:

Olenka [21]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.

Semmy [17]3 years ago

3 0

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

You might be interested in

Andrew

PilotLPTM [1.2K]

Let's say Bailey takes "b" days to paint it.

and Andrew takes "a" days to paint the same house.

now, Andrew is 6 times faster than Bailey, therefore, if Andrew takes "a" days to do it, Bailey takes then "6a" days, or b = 6a.

now, the year they worked together, they finished it in 7 days.

so, after 1 day then, they have only done 1/7 of the whole work.

and Andrew for one day, has done 1/a of the house, whilst Bailey has done 1/b of the house or 1/(6a).

$\bf \stackrel{\textit{Andrew's rate}}{\cfrac{1}{a}}+\stackrel{\textit{Bailey's rate}}{\cfrac{1}{b}}=\stackrel{\textit{1 day of work}}{\cfrac{1}{7}}
\\\\\\
\cfrac{1}{a}+\cfrac{1}{6a}=\cfrac{1}{7}\impliedby 
\begin{array}{llll}
\textit{let's multiply all by }\stackrel{LCD}{42a}\textit{ to toss the}\\
denominators
\end{array}$

$\bf 42a\left( \cfrac{1}{a}+\cfrac{1}{6a} \right)=42a\left( \cfrac{1}{7} \right)\implies 42+7=6a\implies \cfrac{49}{6}=a
\\\\\\
\stackrel{days}{8\frac{1}{6}}=a
\\\\\\
\textit{how many days will it take Bailey then?}\quad b=6a
\\\\\\
b=6\cdot \cfrac{49}{6}\implies b=\stackrel{days}{49}$

6 0

4 years ago

Karen bought a jacket for$280.80 inclusive of an 8% sales tax.Find the price of the jacket before sales tax was applied.

Serhud [2]

Answer:

$260

Step-by-step explanation:

Actual price + 8% of actual price=$280.80

Let x= actual price

8% of actual price=8/100 of x

=0.08x

x + 0.08x=$280.80