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RUDIKE [14]
3 years ago
6

The length of the rectangle is 5 inches more than twice the length of the side of the square

Mathematics
1 answer:
crimeas [40]3 years ago
3 0

Answer:

The length of Rectangle is (5 + 2 s) inches and                                           width of rectangle is  \dfrac{s^{2} }{5 + 2 s} inches  .

Step-by-step explanation:

Given as :

The length of the rectangle is 5 inches more than twice the length of the side of the square

The area of Rectangle = The area of square

Let the side of the square = s inches

So, The Area of square = side × side

I.e The Area of square = s × s = s²  inches²

Again

Let The length of rectangle = L inches

And The width of rectangle = w inches

So, The Area of Rectangle = ( L × w ) inches²

So, <u>According to question</u>

The length of rectangle = 5 inches + twice length of square side

I.e L = ( 5 + 2 s ) inches

<u>∵ Both The area same</u>

So, L× w = s²

Or, w = \dfrac{s^{2} }{L}

or,  w = \dfrac{s^{2} }{5 + 2 s} inches

So, The measure of length of Rectangle = L = (5 + 2 s) inches and width of rectangle = w = \dfrac{s^{2} }{5 + 2 s} inches

Hence, The measure of length of Rectangle is (5 + 2 s) inches and width of rectangle is  \dfrac{s^{2} }{5 + 2 s} inches  . Answer

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Answer:

  CX = 15√2 inches

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Step-by-step explanation:

In this geometry, all of the triangles are similar:

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Corresponding segments are proportional in similar triangles, so we have ...

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Filling in the numbers, we get

  30/CX = CX/15

  CX² = 15×30

  CX = 15√2 . . . . . exact length of the altitude (inches)

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Similarly, we can form proportions with the legs:

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and

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  AC = 15√6 . . . inches

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<em>Additional comment</em>

You may notice that each of the segments we're interested in is the root of a product involving segments of the hypotenuse. This "root of a product" is called the geometric mean. Here, the three geometric mean relations are ...

  altitude = geometric mean of hypotenuse segments

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Strictly speaking the geometric mean is the n-th root of the product of n items. Here, there are only 2 items, so it is the square root of their product.

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Given

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