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ser-zykov [4K]
3 years ago
5

The length of a rectangle is 59 inches greater than twice the width. If the diagonal is 2 inches more than the​ length, find the

dimensions of the rectangle.
Mathematics
1 answer:
melamori03 [73]3 years ago
5 0
The question is asking us to find the dimensions of the rectangle, which would be the length and width. So, to find this, we must first state our givens, as it is Geometry.
Given: Length of rectangle = 59 + twice the width, diagonal = 2 inches longer than the width

Let's first translate all our givens to numbers. We'll start off by assigning variables that are easy to work with (x, y and z). 
x = width
y = length
z = diagonal
Now that we have done that, we need to translate all our givens into numbers. Here is how that would look like:
y = 2x + 59      ←59 plus twice the width (x)
z = y + 2           ←Diagonal = 2 inches more than width
If we draw a diagram, we can see that the diagonal, length, and width all create a right triangle, which means that we can use the Pythagorean Theorem. By using right triangle postulates and theorems, we can deduce that the diagonal is the hypotenuse. Here is what our setup looks like:
x² + y² = z²
<em />Now, all we need to do is plug in the expressions we created for y and z:
x² + (2x + 59)² = [2 + (2x + 59)²]
When we solve for x, we get x = 20. Now, we just plug the x value back into the y equation to get 99. Therefore, the length equals 99 inches and the width equals 20 inches. Hope this helps and have a great day!
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There are four pairs (m,n) that work: (5,10), (6,6), (8,4), and (12,3).

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3 years ago
What is equivalent to 9x -12 = 36
Andreas93 [3]

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3x - 4 =9

Step-by-step explanation:

divide the entire equation by 3

9x/3 - 12/3 = 36/3

3x - 4 = 9

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How can you find the surface area of a composite solid made up of prisms ? (Help)
sammy [17]
Oh, this is easy. For any prism, you find the surface area by finding the are of all the sides. I will post all surface area formulas here, for reference
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Surface area = 6 × a2




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pi = 3.14
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Sphere:



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Right circular cone:



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8 0
3 years ago
Find the equation of a line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3). (answer in slope-intercept fo
Alla [95]

Answer:

\displaystyle y=-\frac{1}{2}x+4

Step-by-step explanation:

<u>Equation of a Line</u>

We can find the equation of a line by using two sets of data. It can be a pair of ordered pairs, or the slope and a point, or the slope and the y-intercept, or many other combinations of appropriate data.

We are given a line

y - 12 = 2x -8

And are required to find a line perpendicular to that line. Let's find the slope of the given line. Solving for y

y = 2x +4

The coefficient of the x is the slope

m=2

The slope of the perpendicular line is the negative reciprocal of m, thus

\displaystyle m'=-\frac{1}{2}

We know the second line passes through (2,3). That is enough information to find the second equation:

y-y_o=m'(x-x_o)

\displaystyle y-3=-\frac{1}{2}(x-2)

Operating

\displaystyle y=-\frac{1}{2}(x-2)+3

Simplifying

\displaystyle y=-\frac{1}{2}x+4

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8 0
3 years ago
If a polygon has an interior angle of 144, what kind of polygon is it? (find the # of sides first
ikadub [295]
<span>Each Interior Angle = <span>(<span>(Number of Sides -2) • 180 degrees<span>)<span> ÷ (Number of Sides)

Solving for number of sides
</span></span></span></span></span>
<span>Each Interior Angle / 180 = <span>(N -2) <span>/ (N)

144 / 180 = (n-2) / n

144 * n = 180n -360
360 = 36 n

n = 10 the number of sides

Source:
http://www.1728.org/polygon.htm

</span></span></span>
5 0
3 years ago
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