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4 years ago

The perimeter of a rectangle is 22 inches. Find the dimensions if its length is 3 inches greater than its width.

Mathematics

1 answer:

MaRussiya [10]4 years ago

7 0

Answer:

Length: 7

Width: 4

Step-by-step explanation:

We can create a system of equations for this problem, where $w$ is the width and $l$ is the length.

The perimeter of a rectangle is twice its length added to twice its width.

$2l+2w=22$

The length is 3 more than the width:

$l = w+3$

We can now substitute in $w+3$ as $l$ in the equation $2l+2w=22$ .

$2(w+3) + 2w = 22$

Distribute the first terms:

$2w+6+2w=22$

Combine like terms:

$4w+6=22$

Subtract 6 from both sides:

$4w=16$

Divide both sides by 4:

$w = 4$

Now we know that w = 4. We can now substitute this inside an equation to find $l$ .

$l = w+3\\\\l = 4+3\\\\l=7$

Hope this helped!

You might be interested in

The length of an equilateral triangle is increased by 5 cm. The perimeter of the new triangle is 72 cm. What is the side length

Igoryamba

Answer:

19cm

Step-by-step explanation:

An equilateral triangle is a triangle where the length of the 3 sides are the same.

the perimeter is the sum of the 3 sides

for example, if the length of the side of the an equilateral triangle is 5, the perimeter is 5 x 3 = 15

let x = unknown length of side

length after increase = x + 5

(x + 5) x 3 = 72

divide both sides of the equation by 3

x + 5 = 24

subtract 5 from both sides of the equation

x = 24 - 5 = 19cm

6 0

3 years ago

Write a linear equation that passes through the two points (-6, -7) and (3, -4).

Phantasy [73]

linear equation that passes through the two points (-6, -7) and (3, -4) is $y=\frac{1}{3}x-5$

Step-by-step explanation:

We need to write the equation that passes through the two points (-6, -7) and (3, -4).

The equation can be written is point slope form.

The standard form of point slope equation is:

$y=mx+b$

where m is the slope and b is the y-intercept

Finding slope m:

Slope can be found by using formula:

$slope = \frac{y_{2}-y_{1}}{x{2}-x_{1}} \\Where\,\, y_{2}=-4,y_{1}=-7,x{2}=3,x_{1}=-6\\slope =\frac{-4-(-7)}{3-(-6)}\\slope=\frac{-4+7}{3+6}\\slope=\frac{3}{9}\\slope=\frac{1}{3}$

So, slope is $\frac{1}{3}$

Now finding y-intercept b

Putting slope $\frac{1}{3}$ and point(-6,-7)

$y=mx+b\\x=-6,y=-7,m=\frac{1}{3} \\-7=\frac{1}{3}(-6)+b\\-7=-2+b\\b=-7+2\\b=-5$

So, value of b is -5

Putting values to find the equation:

$y=mx+b\\m=\frac{1}{3} and b=-5\\y=\frac{1}{3}x-5$

So, linear equation that passes through the two points (-6, -7) and (3, -4) is $y=\frac{1}{3}x-5$

Keywords: Linear Equation,

Learn more about Linear Equation at:

#learnwithBrainly

5 0

3 years ago

Please answer fastly (4/5 +2) (3- 2/3)

MaRussiya [10]

Answer:

exact form: 98/15 decimal form: 6.53 mixed number form: 6 8/15

Step-by-step explanation:

hope this helped

6 0

3 years ago

How do i solve for x and y here?

Citrus2011 [14]

Hope this would help you

4 0

3 years ago

How do you use change of base formula

nikdorinn [45]

Answer:

According to the change-of-base formula, we can rewrite the log base 2 as a logarithm of any other base. Since our calculators can evaluate the natural log, we might choose to use the natural logarithm, which is the log base e.

Step-by-step explanation:

6 0

3 years ago