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kumpel [21]
3 years ago
11

Steve made a sign for his room that is shaped like a triangle. It is 4.5 feet long and 3 feet high. He wants to make another sig

n that is shaped like a triangle and similar to the first sign. The new sign will be 4 feet high.
Part A

Write a proportion that Steve can use to find the length, x, of the new sign.

Part B

What is the length, in feet, of the new sign? Make sure to show your work and explain your reasoning.
Mathematics
1 answer:
Fed [463]3 years ago
6 0

Answer: PART A : \frac{4.4}{x} = \frac{3}{4}

PART B : 5.9 FEET

Step-by-step explanation:

Length of the first sign = 4.4 feet

height of the first sign = 3 feet

Length of the second sign = x feet

height of the second sign = 4 feet

If two shapes are similar , then the ratio of their sides are equal,

That is ;

\frac{h_{1}}{h_{2} } = \frac{L_{1}}{L_{2} }

PART A

\frac{4.4}{x} = \frac{3}{4}

PART B

\frac{4.4}{x} = \frac{3}{4}

cross multiplying , we have

3x = 4.4 x 4

3x = 17.6

Divide through by 3

x = 17.6/3

x = 5.86666666666667

x≈ 5.9 feet

Therefore , the length of the new sign is 5.9 feet

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Robert needs to cut four shelves from a board that is 2.5 meters long. The second shelf is 18 cm longer than twice the length of
g100num [7]
STEP 1:
convert meters to centimeters
100 cm= 1 meter

= 100 cm/m * 2.5 m
= 250 cm


STEP 2:
x= length of first shelf
2x+18= length of second shelf
x-12= length of third shelf
x+4= length of fourth shelf

since the whole board has to be used, add lengths of all shelves and set it equal to the whole length of the board (250 cm).

x + (2x+18) + (x-12) + (x+4)= 250 cm
combine like terms
5x + 10= 250
subtract both sides by 10
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divide both sides by 5
x= 48


STEP 3:
find length of second shelf
= 2x + 18
= 2(48) + 18
= 114 cm


CHECK:
x + (2x+18) + (x-12) + (x+4)= 250
48 + (2(48)+18) + (48-12) + (48+4)= 250
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48 + 114 + 36 + 52= 250
250= 250


ANSWER: Shelf two is 114 cm.

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