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mrs_skeptik [129]
3 years ago
10

Mr.Winston is adding a sunroom to his house. After laying the foundation and building the frame he double checks his measurement

s. Mr.Winston found that his 14 ft by 13 ft (rectangular) sunroom had a diagonal measurement of 20 ft. Why is Mr.Winston in trouble?
Mathematics
1 answer:
STALIN [3.7K]3 years ago
4 0

Answer:

The measurement of the diagonal is NOT CORRECT.

So, Mr. Winston is in trouble.

Step-by-step explanation:

The length of the rectangular room = 14 ft

The width of the room  = 13 ft

Let us assume the length of the diagonal  = m

Now,a s the room is a rectangle so, by PYTHAGORAS THEOREM:

(LENGTH)^2 + (WIDTH)^2 = (DIAGONAL)^2

⇒(14)^2 + (13)^2 = (m)^2\\\implies m = \sqrt{196 +  169}  = \sqrt{365} = 19.10

or, the length of the diagonal of the room is 19.10 ft

But here, given the sun room had a diagonal measurement of 20 ft.

Hence, the measurement of the diagonal is NOT CORRECT. So, Mr. Winston is in trouble.

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<h3>Distributive Property</h3>

The distributive property lets you group or ungroup terms using parentheses. It lets you multiply an external factor by every term in parentheses, expressing the result as a sum:

... a(b + c) = ab + ac . . . . . . factor <em>a</em> multiplies the terms <em>b</em> and <em>c</em>

and it lets you remove a common factor from different terms, putting that factor outside parentheses:

... ab + ac = a(b + c)

The letters <em>a</em>, <em>b</em>, <em>c</em> here can stand for any number or expression.

<h3>Homework</h3>

20. To do this problem, you need to eliminate the parentheses using the distributive property. Then, "collect terms," which is another application of the distributive property. The external factor outside the parentheses is (-2/3). Multiply that by each term in parentheses, and add the results.

After that, recognize that c is a factor of two of the terms. Add their coefficients to simplify that sum to one term.

-\dfrac{2}{3}(12c-9)+14c=\left(-\dfrac{2}{3}\right)(12c)+\left(-\dfrac{2}{3}\right)(-9)+14c=-8c+6+14c\\\\=c(-8+14)+6\\\\=6c+6

22. You are to evaluate the expression with x=2 two ways: as is, and after you simplify it by combining like terms.

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I prefer simplifying the expression first. The number of calculations and chances for error are reduced.

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