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Olegator [25]
3 years ago
6

A rectangle is inscribed in a right isosceles triangle, such that two of its vertices lie on the hypotenuse, and two other on th

e legs. What are the lengths of the sides of the rectangle, if their ratio is 5:2, and the length of the hypotenuse is 45 in? (Two cases)
Case 1) Blank, Blank, Blank
Case2) Blank, Blank, blank
What goes in these blanks?

Mathematics
1 answer:
Ronch [10]3 years ago
6 0
Refer to the attachment for the diagram of the problem.

Let us call the two identical sides of the isosceles triangle with s. Since we know that the hypotenuse measures 45 inches, we can find s by using the Pythagorean Theorem:
45^{2} = s^{2}+ s^{2}
45^{2} = 2s^{2}
45^{2} = 2s^{2}
1012.5 = s^{2}
s=31.82

We can notice that the figure will have similar triangles with the smaller triangle having one length equal to 5x. We then compute for the equivalent hypotenuse of the smaller triangle (denoted as y).
\frac{31.82}{5x} = \frac{45}{y}
y=7.07x

We can then solve for the value of x by applying the Pythagorean Theorem in the smaller triangle.
(7.07x)^{2} = (5x)^{2}+ (31.82-2x)^{2}
50x^{2} = 25x^{2}+ 1012.5-127.28x+4x^{2}
0= -21x^{2}-127.28x+1012.5
x=4.55,-10.61

We ignore the negative value since there is no negative side. x is therefore 4.55 thus the dimensions of the rectangle would be 22.75 and 9.1. For the other case, the dimensions would simply be inverted since we would be dealing with a rectangle with its width longer than its length.

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german
Hello,

Let's calculate the radius:

r²=5²+7²=74

The circle's equation is (x+5)²+(y+7)²=74

Answer C
5 0
3 years ago
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How many times can 8 go into 9
AnnZ [28]

Answer:

Once

Step-by-step explanation:

8 can only go into 9 once, if you were to do it a second time, there would be a remainder of 7.

8 0
3 years ago
Can Somebody Please Help
Free_Kalibri [48]

Answer:

We have to put the data for purchased item in a frequency table.

Step-by-step explanation:

The diagram is attached below.

Firstly we have to see that how many customers fall under range 0 to 5.

Then 5 to 10.

Then 10 to 15.

Finally

15 to 20.

If we go through the items purchased by customers we can see that item ranges from 0 to 5 have 4 customers.

Item purchased range from 5 to 10 have 2 customers.

Item purchased range from 10 to 15 have 7 customers.

Item purchased range from 15 to 20 have 1 customers.

Total number of customers = 14

As we have total 14 number of customers and they have varied quantity of items purchased.

6 0
3 years ago
When QS=6x and CS=5x-8, what is AB?
patriot [66]

Answer:

AB = x+ 8

Step-by-step explanation:

Given : QS=6x and CS=5x-8

From the given figure,

QS = QC + CS

We are given with  QS  and CS

Replace it the above equation

6x = QC + 5x -8

Solve for QC

Subtract 5x on both sides

x = QC + -8

Add 8 on both sodes

QC= x + 8

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QC = AB

So AB = x+ 8


4 0
3 years ago
Mary has 12 video games. She purchases five new video games each month as part of a video game club.
Oxana [17]

Answer:

The answer to your question is:  V = 12 + 5n

Step-by-step explanation:

Data

Video games right now = 12

She purchases 5 video games each month

Equation = ?

# of video games in n month = V

Process

           - Consider the initial amount of video games

                                   V = 12

           - Now, consider the number of video games the buys each month and the months

                                 5n

           - Finally, join both terms

                                  V = 12 + 5n

8 0
3 years ago
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