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V125BC [204]
3 years ago
11

The longest side of a triangle is 3 in. longer than the shortest side. The medium side is 2 in. longer than the shortest side. I

f the perimeter of the triangle is 26 ​in., what are the lengths of the three​ sides?
Mathematics
2 answers:
sweet [91]3 years ago
8 0

Answer: shortest side = 7 in

Medium side = 9 in

The longer side = 10 in

Step-by-step explanation:

Let x represent the smallest side of the triangle.

The longest side of a triangle is 3 in. longer than the shortest side. It means that the length of the longest side is x + 3

The medium side is 2 in. longer than the shortest side. It means that the length of the medium side is x + 2. If the perimeter of the triangle is 26 ​in, it means that

x + x + 2 + x + 3 = 26

3x + 5 = 26

3x = 26 - 5 = 21

x = 21/3 = 7

The medium side is x + 2 = 7 + 2 = 9 in

The longer side is x + 3 = 7 + 3 = 10 in

Olenka [21]3 years ago
7 0

s = length of the shortest side of the triangle

m = length of the medium side of the triangle

l = length of the longest side of the triangle

(you can use different variables like l, w, h, x, y.......)

Perimeter(P) of a triangle is the total sum of the sides, in this case:

P = s + m + l

You know:

P = 26in

l = s + 3     [longest side is 3in longer/more than(addition) the shortest side]

m = s + 2   [medium side is 2in longer than the shortest side]

To find the lengths of the three sides, you can do this:

P = s + m + l         Substitute/plug in what you know. So plug in 26 into "P" since P = 26, plug in (s + 3) into "l" since l = s + 3, and plug in (s + 2) into "m" since m = s + 2

26 = s + (s + 2) + (s + 3)     Combine like terms (like terms have the same variable and power/exponent)

26 = 3s + 5   To find "s", isolate/get the variable "s" by itself. Subtract 5 on both sides

21 = 3s      Divide 3 on both sides to get "s" by itself

7 = s        

Now that you found s, you can use it to find the other sides

m = s + 2          Substitute/plug in 7 into "s" since s = 7

m = 7 + 2

m = 9

l = s + 3    Plug in 7 into "s"

l = 7 + 3

l = 10

The longest side is 10 inches, the medium side is 9 inches, the shortest side is 7 inches

PROOF

P = s + m + l

P = 7 + 9 + 10

P = 26 inches

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gtnhenbr [62]

Answer:

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Step-by-step explanation:

Using the sine ratio in the right triangle, that is

sinx = \frac{opposite}{hypotenuse} = \frac{6}{10} , then

x = sin^{-1} (\frac{6}{10} ) ≈ 36.9° ( to 1 dec. place )

7 0
3 years ago
if a rectangle has an area of 30 square meters and a perimeter of 34 meters . what is the dimensions of the rectangle?
timama [110]
P=2(L+W)  and P=34 so

2(L+W)=34

L+W=17 so we can say

L=17-W

A=LW using L from above

A=(17-W)W

A=17W-W^2 and A=30 so

30=17W-W^2

W^2-17W+30=0

W^2-2W-15W+30=0

W(W-2)-15(W-2)=0

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7 0
3 years ago
4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.
nikitadnepr [17]

Answer:

\sum_{n=0}^9cos(\frac{\pi n}{2})=1

\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0

\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}

Step-by-step explanation:

\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))

=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})

=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1

2nd

\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}

=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0

3th

\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))

=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}

What we use?

We use that

e^{i\pi n}=cos(\pi n)+i sin(\pi n)

and

\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}

6 0
3 years ago
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LUCKY_DIMON [66]

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7 0
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Nimfa-mama [501]
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Step-by-step explanation:

6 0
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