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Vinil7 [7]
3 years ago
10

Eighth grade

Mathematics
1 answer:
lutik1710 [3]3 years ago
8 0

The length and width of the rectangle are 19 inches and 13 inches respectively.

<u>Solution:</u>

Given that , A rectangular sheet of metal has an area of 247 square inches. Its perimeter is 64 inches.

Let the length of rectangle be a and width of rectangle be b.  

<em><u>The area of rectangle is given as: </u></em>

area = length \times width

\text { Then, area } \rightarrow a b=247

<em><u>The perimeter of rectangle is given as:</u></em>

Perimeter = 2(length + width)

Then 2(a + b) = 64

a + b = 32 ⇒ (1)

\begin{array}{l}{\text { Now we know that, }(a-b)^{2}=(a+b)^{2}-4 a b} \\\\ {\text { Then, }(a-b)^{2}=32^{2}-4 \times 247} \\\\ {(a-b)^{2}=1024-988} \\\\ {a-b=\sqrt{36}}\end{array}

a – b = 6 ---- (2)

Now solve (1) and (2)

2a = 38

a = 19

Then, 19 + b = 32  

b = 32 – 19 = 13  

hence, the length and width of the rectangle are 19 inches and 13 inches respectively.

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In the question ,

an mathematical phrase is given , that is "Twelve more than the quotient of six divided by three" .

we have to translate it into mathematical expression ,

So , the term quotient of six divided by three is written as 6 ÷ 3 .

and phrase " more " is represented by " + " ,

Hence the given phrase,  "Twelve more than the quotient of six divided by three" is  (6 ÷ 3) + 12 .

Therefore , The given phrase on translation to math expression is (6 ÷ 3) + 12 , the correct option is (a) .

The given question is incomplete , the complete question is

Translate the phrase into a math expression , "Twelve more than the quotient of six divided by three" .

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(b) 6÷(3+12)

(c) (3÷6)+12

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Tristán wants to build a square garden in his backyard if the garden is going to be 64 ft2 how many feet of material will he nee
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Answer:

Tristan will need 32 feet of material for the perimeter of the garden.

Step-by-step explanation:

Given that

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We know that for calculation of perimeter, length of side of square is required which is not directly given in the question. The area will be used to calculate length of side and then length will be used to calculate the perimeter.

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Tristan will need 32 feet of material for the perimeter of the garden.

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