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mote1985 [20]
3 years ago
9

Adam cut a piece of string 42 inches long into 2 pieces. The ratio of the length of the 2 peices is 3:4, what is the length, to

the nearest inch, of the shorter piece
Mathematics
1 answer:
jek_recluse [69]3 years ago
6 0

Answer:

Shorter piece length is 18 inches

Step-by-step explanation:

Let's marked first piece with x and second with y

x + y = 42

Given ratio is x : y = 3 : 4

From this proportion we get

x = 3 c  and y = 4 c   where c is coefficient of proportionality

when we replace this in initial equation we get

3 c + 4 c = 42 => 7 c = 42 => c = 42/7 = 6    c = 6

x = 3 · 6 = 18 inches  and z = 4 · 6 = 24 inches

shorter piece is x = 18 inches

God with you!!!

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Answer:

c) A rectangle with width of 9 mm and length of 45 cm.

d) A rectangle with width of 10 cm and length of 44 cm.

Step-by-step explanation:

Given:

Length of the rectangle = 32 in.

Width of the rectangle = 8 in.

First we will find the ratio of length by width.

\frac{length}{width}= \frac{32}{8} = \frac{4}{1} \ \ \ \ equation \ 1

Now we need to find from the given Option which rectangles are not similar to Carl's Rectangle.

So we will check for each.

a) A rectangle with width of 23 cm and length of 92 cm.

we will find the ratio of length by width.

\frac{length}{width}= \frac{92}{23} = \frac{4}{1} \ \ \ \ equation \ 2

By Definition of Similar rectangles which states that;

"When ratio of the dimension of 2 corresponding rectangles are equal then the 2 rectangles are said to be similar."

Now Comparing equation 1 and equation 2 we get;

equation 1 = equation 2

Hence This rectangle is similar to Carl's rectangle.

b) A rectangle with width of 2.5 inch and length of 10 inch.

we will find the ratio of length by width.

\frac{length}{width}= \frac{10}{2.5} = \frac{4}{1} \ \ \ \ equation \ 2

By Definition of Similar rectangles which states that;

"When ratio of the dimension of 2 corresponding rectangles are equal then the 2 rectangles are said to be similar."

Now Comparing equation 1 and equation 2 we get;

equation 1 = equation 2

Hence This rectangle is similar to Carl's rectangle.

c) A rectangle with width of 9 mm and length of 45 cm.

we will find the ratio of length by width.

\frac{length}{width}= \frac{45}{9} = \frac{5}{1} \ \ \ \ equation \ 2

By Definition of Similar rectangles which states that;

"When ratio of the dimension of corresponding rectangles are equal then the 2 rectangles are said to be similar."

Now Comparing equation 1 and equation 2 we get;

equation 1 \neq equation 2

Hence This rectangle is not similar to Carl's rectangle.

d) A rectangle with width of 10 cm and length of 44 cm.

we will find the ratio of length by width.

\frac{length}{width}= \frac{44}{10} = \frac{11}{5} \ \ \ \ equation \ 2

By Definition of Similar rectangles which states that;

"When ratio of the dimension of corresponding rectangles are equal then the 2 rectangles are said to be similar."

Now Comparing equation 1 and equation 2 we get;

equation 1 \neq equation 2

Hence This rectangle is not similar to Carl's rectangle.

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