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tamaranim1 [39]
3 years ago
13

A rectangular poster is 3 times as long as it is wide. A rectangular banner is 5 times as it is wide. Both the banner and the po

ster have perimeters of 24 inches. What are the lengths and widths of the poster and the banner?
Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
8 0

The length and width of poster are 9 inches and 3 inches respectively and length and width of banner are 10 inches and 2 inches respectively

<u> Solution:</u>

Given, A rectangular poster is 3 times as long as it is wide.  

Rectangular banner is 5 times as long as it is wide.  

Both the banner and the poster have perimeters of 24 inches

Let, the width of poster be p, then its length will be 3p

And, the width of banner be b, then its length will be 5b

Now, according to given information,

Perimeter of poster = 24 inches and perimeter of banner = 24 inches

2(length of poster + width of poster) = 24

2(3p + p) = 24

2(4p) = 24

8p = 24

p = 3

And 2(length of banner + width of banner) = 24

2(5b + b) = 24

2(6b) = 24

12b = 24

b = 2

So, width of poster is 3 inches, then length of poster is 3p = 3 x 3 = 9 inches

And, width of banner is 2 inches, then length of banner is 5b = 5 x 2 = 10 inches

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8 and 1 half pounds = 8.5 Ibs

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2 years ago
If the second number is subtracted from the sum of the first number and 2 times the third number, the result is 1. The thrid num
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Answer:

<h2>x = 0, y = 5, z = 3</h2>

Step-by-step explanation:

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\left\{\begin{array}{ccc}x+(2)(3)+(2)(-2x)-y=1\\x+3y+3-2x=18&\text{subtract 3 from both sides}\end{array}\right\\\left\{\begin{array}{ccc}x+6-4x-y=1&\text{subtract 6 from both sides}\\(x-2x)+3y=15\end{array}\right\\\left\{\begin{array}{ccc}(x-4x)-y=-5\\-x+3y=15\end{array}\right\\\left\{\begin{array}{ccc}-3x-y=-5&\text{multiply both sides by 3}\\-x+3y=15\end{array}\right

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7 0
3 years ago
ABCD diagonals intersect at E. If m∠BAC=4x+5 and m∠CAD=5x-14, then find m∠CAD.
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Answer: m∠CAD = 81°

Step-by-step explanation: <u>Diagonal</u> is a line that unites opposite sides.

ABCD is a prallelogram. One property of diagonal in a parallelogram is it separates the parallelogram in 2 congruent triangles.

The figure below shows ABCD with its diagonals.

Since diagonal divides a parallelogram in 2 congruent triangles, it means the internal angles are also congruent. So

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Then, m∠CAD is

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Hope that helps. Let me know if you have any questions.

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