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mezya [45]
3 years ago
13

A parallelogram has sides 10m and 12m and an angle of 45°. Find the distance between the 12m-sides.

Mathematics
1 answer:
stich3 [128]3 years ago
4 0

Answer:

The distance between 12m-sides is 5\sqrt{2}m.

Step-by-step explanation:

It is given that the parallelogram has sides 10m and 12m and an angle of 45°.

Draw an altitude from one 12m side to another 12 m side as shown in below figure.

The opposite angles of parallelogram are same. Two angles are obtuse angles and two are acute angle.

Since angle C is acute angle therefore it must be 45 degree.

\sin\theta=\frac{perpendicular}{hypotenuse}

\sin C=\frac{BE}{BC}

\sin(45^{\circ})=\frac{d}{10}

\frac{1}{\sqrt{2}}=\frac{d}{10}

\frac{10}{\sqrt{2}}=d

\frac{10}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}=d

\frac{10\sqrt{2}}{2}=d

5\sqrt{2}=d

Therefore the distance between 12m-sides is 5\sqrt{2}m.

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Kim wants to buy art supplies that normally costs $50, but are on sale for 20% off. What is the sale price for the art supplies?
stepan [7]

Answer:

$40

Step-by-step explanation:

100% - 20% = 80%

80% of $50 = 0.8 × $50 = $40

4 0
2 years ago
The width of a rectangle is 3 less than its length find the width of the rectangle if its perimeter is 26ft
Marta_Voda [28]

The width of rectangle is 5 feet.

Let us assume the length of rectangle to be x. So, the width of rectangle will be (x - 3).

Now, as per the known fact, perimeter, length and width of rectangle are related by the formula -

Perimeter = 2 × (length + width)

Keep the values in formula to find the value of width

26 = 2 × (x + x - 3)

Performing addition of variables inside the bracket

26 = 2 × (2x - 3)

Shifting 2 to other side of equation to find the value of x

2x - 3 = \frac{26}{2}

Performing division to find the value of x

2x - 3 = 13

Shifting 3 to other side of equation to find the value of x

2x = 13 + 3

Performing addition to find the value of x

2x = 16

Shifting 2 as denominator to other side of equation to find the value of x

x = \frac{16}{2}

Performing division to find the value of x

x = 8

So, length of rectangle is 8 feet

Width of rectangle = x - 3

Width of rectangle = 8 - 3

Width of rectangle = 5 feet

Hence, the width of rectangle is 5 feet.

Learn more about calculation involving rectangle -

brainly.com/question/24571594

#SPJ4

7 0
1 year ago
Answer the question about the angles below.
kaheart [24]
To find angle Y, take 180 degrees (linear pair) minus 35 degrees (angle X).
180-35=145 degrees
Angle Y=145 degrees
Angle W is also 145 degrees since it’s a vertical angle to Angle Y.
To find angle N, take 90 degrees (complementary angle) minus 55 degrees (angle M).
90-55=35 degrees
Angle N=35 degrees
Hope this helped!
3 0
3 years ago
Please help me with this!..
ch4aika [34]

Answer:

I think it would be 12

Step-by-step explanation:

3 0
3 years ago
The owner of a flower shop sells 18 roses gor 90$ what is the cost in dollars per rose
Sunny_sXe [5.5K]
The equation would be 90/18 which would give you the cost of 5 dollars per rose
4 0
3 years ago
Read 2 more answers
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