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Alex Ar [27]
3 years ago
15

The diagonal of the floor of a square room is 6 meters.what is the length of a side of the room? round to the nearest tenth.

Mathematics
1 answer:
shutvik [7]3 years ago
4 0
Side of the room = x.
From the right triangle, where sides of the square are legs of the right triangle, and the diagonal of the square is a hypotenuse of the right triangle.
x²+x²=6²
2x²=36
x²=18
x=√18 =√(2*9)=3√2≈4.2m
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I will mark brainliest IF CORRECT
umka2103 [35]

Answer:

1 - (π/6) - (√3/4)

Step-by-step explanation:

First, calculate the area of ABCD. That's just 1*1 = 1 un^{2}

Then, we are told that arcs BD and AC are circular, meaning they are portions of a circle. Therefore, let's redraw this image a little. Look below for the image.

Essentially, what I've done is created an equilateral triangle and two sectors. You may be wondering why the triangle is equilateral. Well, we firstly know it's isosceles because the two original arcs are circular and congruent. Their overlap creates two congruent lines that can be extend from point M to the vertices A and D. These two lines also happen to be radii of the quarter circles because the two sectors have AM AND AD as radii. AM and AD = 1, so AMD is an equilateral triangle.

Draw altitude OD. This is a right angle. Since equilateral triangles are also isosceles triangles, and isosceles triangles have the property of sharing the median to base and altitude to base, we can say that OD = \frac{1}{2} AD = \frac{1}{2}. MD = 1, so this triangle is a 30-60-90 triangle. Why? This is because of the 30º angle converse theorem. The shorter leg is half of the hypotenuse MD, so <OMD is a 30º angle, making <ODM a 60º angle and inevitably <MDC a 30º angle (because <D is a right angle) and <ABM as well because the two sectors are congruent.

Because m<ABM = m<MDC = 30º, these two sectors are 30/360 of the individual circles or 1/12 of the original circles, which have areas of π (because 1^2*π = π). Each is 1/12π, combined they are 1/6π.

The area of the equilateral triangle is √3/8. This is because MO can be calculated, using the 30-60-90 ratios, to be √3/2. (1 * √3/2)/2 = (√3/2)/2 = √3/4; this uses the area of a triangle. Now, time to calculate the shaded area.

The area of the square is 1, the area of the sectors π/6, and the equilateral triangle √3/4. Subtract the equilateral triangle and sectors' areas from the area of the square to be left with the remaining shaded part. 1-(π/6)-(√3/4) is your final answer. To put that a little more cleanly below in the image.

Hope this helps, have a great day.

3 0
2 years ago
Evaluate the expression 5t + 2m for m = 7 and t = 2.
pantera1 [17]

Answer:

<h3>The answer is 24</h3>

Step-by-step explanation:

5t + 2m

m = 7 t = 2

Substitute the above values into the expression

That's

5(2) + 2(7)

10 + 14

24

Hope this helps you

5 0
3 years ago
16.The least common denominator of 1/2, 1/8, and 1/10 isO A. 10.OB. 80.C. 40.D. 16.nMark for review Awill be biabliabted on the
tangare [24]

Given

The numbers, 1/2, 1/8, and 1/10.

To find: The least common denominator.

Explanation:

It is given that,

1/2, 1/8, and 1/10 .

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Therefore, the LCM is,

\begin{gathered} LCM=2\times2\times2\times5 \\ =40 \end{gathered}

Hence, the least common denominator is 40.

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The second car is 30 minutes
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strojnjashka [21]

Answer:

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Step-by-step explanation:

I'm not sure how to explain this, but if there is a negative exponent, then it can be written like this, as the denominator of a fraction.

5 0
3 years ago
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