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maw [93]
3 years ago
9

Scale on the blue print drawingOf a house show 6 cm represents 3 m what number of centimeters on the blueprint represents actual

distance of 27 m
Mathematics
1 answer:
iVinArrow [24]3 years ago
5 0

Answer:

54 cm on the blueprint represents actual distance of 27 m.

Step-by-step explanation:

Scale on the blue print drawing of a house show 6 cm represents 3 m.

So, the proportion is \frac{6}{300} = \frac{1}{50} {Since, 3 m = 300 cm.}

Hence, the original dimensions of the house is reduced in the ratio \frac{1}{50} in the blue print drawing.

Then, 27 m i.e. 2700 cm will be represented in the drawing by 2700 \times \frac{1}{50} = 54 cm.

Therefore, 54 cm on the blueprint represents actual distance of 27 m. (Answer)

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A rectangular field is 75 yards wide and 105 yards long
nika2105 [10]

Answer:

width = 72 yards

length = 108 yards

Step-by-step explanation:

Given:

  • Width = 75 yards
  • Length = 105 yards

<u>Area of the field</u> with the given values:

\begin{aligned}\textsf{Area of a rectangle}&=\sf width \times length\\& = \sf 75 \times 105\\& = \sf 7875\:\: yd^2\end{aligned}

To maintain the <u>same perimeter</u>, but <u>change the area</u>, either:

  • decrease the width and increase the length by the same amount, or
  • increase the width and decrease the length by the same amount.

In geometry, length pertains to the <u>longest side</u> of the rectangle while width is the <u>shorter side</u>.  Therefore, we should choose:

  • decrease the <u>width</u> and increase the <u>length</u> by the <u>same amount</u>.

<u>Define the variables</u>:

  • Let x = the amount by which to decrease/increase the width and length.

Therefore:

\implies \sf width \times length < 7875\:\:yd^2

\implies (75-x)(105+x) < 7875

Solve the inequality:

\begin{aligned}(75-x)(105+x) & < 7875\\7875-30x-x^2 & < 7875\\-x^2-30x & < 0\\-x(x+30) & < 0\\x(x+30) & > 0\\\implies x & > 0 \:\: \textsf{ or }\:\:x < - 30\end{aligned}

Therefore, as distance is positive only and the maximum width is 75 yd (since we are subtracting from the original width):

\begin{cases}\textsf{width} = 75 - x\\\textsf{length} = 105 + x\end{cases}

\textsf{where } 0 < x < 75

Therefore, to find the width and length of another rectangular field that has the same perimeter but a smaller area than the first field, simply substitute a value of x from the restricted interval into the found expressions for width and length:

<u>Example 1</u>:

  • Let x = 3

⇒ Width = 75 - 3 = 72 yd

⇒ Length = 105 + 3 = 108 yd

⇒ Perimeter = 2(72 + 108) = 360 yd

⇒ Area = 72 × 108 = 7776 yd²

<u>Example 2</u>:

  • Let x = 74

⇒ Width = 75 - 74 = 1 yd

⇒ Length = 105 + 74 = 179 yd

⇒ Perimeter = 2(1 + 179) = 360 yd

⇒ Area = 1 × 179 = 179 yd²

4 0
1 year ago
Read 2 more answers
|x+7|&gt;3<br><br> help me pleaseeee
Nady [450]

Answer:

x>-4

Step-by-step explanation:

|x+7| is just x+7

x+7>3

-7 on both sides

x>-4

5 0
3 years ago
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The area of an artist square canvas can hold 113 square square inches of paint. What is the approximate length of one side of th
Pavel [41]

Answer:

The approximate length of one side of the canvas (approximate to the nearest hundredth inch)= 10.63

Step-by-step explanation:

There are two ways to solve this problem . One is the use of the calculator and the other is the use of the fraction.

Now the square has equal sides length = breadth .

So we can simply find the length on one side by taking square root with the help of the calculator .

So when you press the symbol of square root after entering the number 113 we get the answer 10.63

Square = Length * breadth

Square = Length * length

Square = L²

One side =√ L²= L so √113= 10.63

The approximate length of one side of the canvas (approximate to the nearest hundredth inch)= 10.63

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4. Mary has 21 coins whose total value is Kshs. 72. There are twice as many five
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Answer:

Mary has  

3 10

shilling coins.

Step-by-step explanation:

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12 first-year teachers and 28 experienced teachers attended a school staff meeting meeting. What percentage of the teachers in t
joja [24]

Answer:

4.8%

Step-by-step explanation:

28+12=40

40÷100=0.4

1% - 0.4 teachers

0.4×12=4.8

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