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3 years ago

Find w and y, will give brainliest for the correct answer

Mathematics

1 answer:

Alex Ar [27]3 years ago

7 0

Answer: w=12, y=6√3

Step-by-step explanation:

Looking at the figure, we can split the triangle into 2 separate triangles. One on the left and one on the left. The triangle on the right is a 30-60-90 triangle. For this triangle, the hypotenuse is 2x in length. This is directly opposite of the right angle. The leg opposite to 30° is x in length. The leg opposite 60° is x√3 in length. Once you know the length of one side, you can plug in x to find the length of the other legs.

In this case, w and y are located on the same 30-60-90 triangle. Normally we would focus on that triangle to find our values, but in this instance, we don't have any values. We have to use the left triangle to find the leg that both triangles share.

The left triangle is a 45-45-90 triangle. For this triangle, the legs opposite of 45° is x in length. The hypotenuse is x√2. Since we know the hypotenuse, we can use it to find x.

x√2=8

x=8/√2

x=5.7 or 6 [Let's use 6 so that it is easier to work with a whole number]

Now that we know x, we can find w and y. Going back to the right triangle, we know the hypotenuse is 2x. We plug in 6 to find the length.

w=2x

w=2(6)

w=12

We know the leg opposite of 60° is x√3. We can plug in x.

y=6√3

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3 years ago

A circle with a radius of 5 is inscribed in a equilateral triangle. What is the area of the triangle's area minus the circle's a

Aleonysh [2.5K]

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3 years ago

What is the area of the trapezoid

irga5000 [103]

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3 years ago

Read 2 more answers

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Sergio039 [100]

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3 years ago

A fence is to be built to enclose a rectangular area of 450 square feet. The fence along three sides is to be made of material t

Mila [183]

Answer:

The short side is _15___ft and the long side is ___30___ ft.

Step-by-step explanation:

As fence is built in a rectangular area, so we can consider

Let

x be the length of the rectangle

y be width of the rectangle

Given area of rectangle is = 450 ft²

Formula for area of rectangle = Length x width

450 ft² = xy

Solve for y

y = 450/x

now according to given condition

three sides of the fence costs $5 per foot and for the fourth side costs$15 per foot.

We have two condition either the fourth side be x or y

So condition 1: Three sides =(x,y,x) 4-th side = y.

So we can write as 5x,5y,5x and 15 y

Cost C = 5x +5y+5x+15y

= 10x+ 5y+15y

= 5(2x+y) +15y----------------equation 1

= 10x +20y

Adding value of y 450/x

= 10x + 20(450/x)

= 10x + 9000/x

For minimum cost, we can consider the cost to be 0

0 = 10x + 9000/x

Dividing and multiplying by -x/x

0 = -10 +9000/x²

10 = 9000/x²

10x² = 9000/

x²= 900

x = 30

so y = 450/x = 450/30= 15 ft

so adding the values of x and y in equation 1 we will have

cost C= 5(2x+y) +15y----------------equation 1

cost is = 5(2(30)+15) +15(15)

= $600 is the cost

X= 30 y =15

So condition 2: Three sides =(y,x,y) 4-th side = x.

So we can write as 5y,5x,5y and 15 x

Cost C = 5y +5x+5y+15x

= 5x+ 10y+15x

= 5(x+2y) +15x----------------equation 2

= 20x +10y

Adding value of y= 450/x

= 20x + 10(450/x)

= 20x + 4500/x

For minimum cost, we can consider the cost to be 0

0 = 20x + 4500/x

Dividing and multiplying by -x/x

0 = -20 +4500/x²

20 = 4500/x²

20x² = 4500

x²= 4500/20= 225

x = 15

so y = 450/x = 450/15= 30 ft

so adding the values of x and y in equation 2 we will have

cost C= = 5(x+2y) +15x----------------equation 2

cost is = 5(15+2(30) +15(15)

= $600 is the cost

y= 30 x=15

so from both conditions satisfy the cost and the two sides are known as length and width

so dimension will be 15 ft by 30 ft

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2 years ago