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prohojiy [21]
2 years ago
10

The perimeter of a rectangle is 60. The length is 10 more than the width. find the length and width

Mathematics
2 answers:
Elenna [48]2 years ago
8 0

Answer:

Width is 10  Length is 20

Step-by-step explanation:

Perimeter = 60

Length = W + 10

P = 2L + 2W                      Write the equation for perimeter

60 = 2(W + 10) + 2W         Substitute your variables

60 = 4W + 20

- 20          - 20                Subtract 20 from both sides

40 = 4W                        Divide both sides by 4

10 = W

Alexxandr [17]2 years ago
5 0

Answer:

width is 10 and length is 20

Step-by-step explanation:

<h2><u>find the length and width</u></h2><h3>perimeter of a rectangle is = 2*length + 2*width</h3>

lets give length and with a variable

length = l

width = w

hence perimeter formula is 2l +2 w

The perimeter of a rectangle is 60. The length is 10 more than the width.

<h3><u>hence this statement helps us to create 2 formulas</u></h3>

l = w + 10

and

2l + 2w = 60

<h3><u>finding w </u></h3>

we can make use of the substitution method. where l is in the second formula place w+ 10 there.

2(w + 10 )+2w = 60

2w + 20  +2w = 60

4w + 20 = 60

4w = 60-20

4w = 40

<u>w = 10 </u>

<u></u>

<h3><u>now we can find l</u></h3>

place the value of w into the first formula so we can find l

l = 10 +10

<u>l = 20</u>

<u></u>

hence this shows that the <u>width is 10 and length is 20 </u>

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Answer:

39

Work:

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We will reverse this equation.

We will start by moving the 2 through inverse operations.

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Now we have the equation

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We will subtract 5

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3 years ago
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3 0
2 years ago
when 6 is subtracted from the square of a number, the result is 5 times the number. Find the negative solution.
sveta [45]

When 6 is subtracted from the square of a number, the result is 5 times the number, then the negative solution is -1

<h3><u>Solution:</u></h3>

Given that when 6 is subtracted from the square of a number, the result is 5 times the number

To find: negative solution

Let "a" be the unknown number

Let us analyse the given sentence

square of a number = a^2

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<em><u>So we can frame a equation as:</u></em>

6 is subtracted from the square of a number = 5 times the number

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<em><u>Let us solve the above quadratic equation</u></em>

For a quadratic equation ax^2 + bx + c = 0 where a \neq 0

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

Here in this problem,

a^2-5 a-6=0 \text { we have } a=1 \text { and } b=-5 \text { and } c=-6

Substituting the values in above quadratic formula, we get

\begin{array}{l}{a=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(-6)}}{2 \times 1}} \\\\ {a=\frac{5 \pm \sqrt{25+16}}{2}=\frac{5 \pm \sqrt{49}}{2}} \\\\ {a=\frac{5 \pm 7}{2}}\end{array}

We have two solutions for "a"

\begin{array}{l}{a=\frac{5+7}{2} \text { and } a=\frac{5-7}{2}} \\\\ {a=\frac{12}{2} \text { and } a=\frac{-2}{2}}\end{array}

<h3>a = 6 or a = -1</h3>

We have asked negative solution. So a = -1

Thus the negative solution is -1

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