Ten boxes are packed tightly in a crate. From above, the packed crate looks like this: [asy] size(4cm); draw((0,10)--(12,10)--(12,0)--(0,0)--cycle,black+3); draw((0,7)--(12,7)); draw((0,4)--(12,4)); draw((4,10)--(4,4)); draw((8,10)--(8,4)); draw((3,4)--(3,0)); draw((6,4)--(6,0)); draw((9,4)--(9,0)); label("$\ell$",(6,10),N); draw((5.3,10+.9)--(0,10+.9),EndArrow(TeXHead)); draw((6.7,10+.9)--(12,10+.9),EndArrow(TeXHead)); label("$w$",(12,5),E); draw((12.9,5.7)--(12.9,10),EndArrow(TeXHead)); draw((12.9,4.3)--(12.9,0),EndArrow(TeXHead)); [/asy] The visible faces of the boxes are all congruent rectangles (that means the ten small rectangles in the diagram are the same shape and size). The top of the crate is $\ell$ inches long by $w$ inches wide, where $\ell\ge w$ (as shown above). What is the ratio $\ell:w$ in simplified form?

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09-01-2022
Mathematics

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Ten boxes are packed tightly in a crate. From above, the packed crate looks like this: [asy] size(4cm); draw((0,10)--(12,10)--(12,0)--(0,0)--cycle,black+3); draw((0,7)--(12,7)); draw((0,4)--(12,4)); draw((4,10)--(4,4)); draw((8,10)--(8,4)); draw((3,4)--(3,0)); draw((6,4)--(6,0)); draw((9,4)--(9,0)); label("$\ell$",(6,10),N); draw((5.3,10+.9)--(0,10+.9),EndArrow(TeXHead)); draw((6.7,10+.9)--(12,10+.9),EndArrow(TeXHead)); label("$w$",(12,5),E); draw((12.9,5.7)--(12.9,10),EndArrow(TeXHead)); draw((12.9,4.3)--(12.9,0),EndArrow(TeXHead)); [/asy] The visible faces of the boxes are all congruent rectangles (that means the ten small rectangles in the diagram are the same shape and size). The top of the crate is $\ell$ inches long by $w$ inches wide, where $\ell\ge w$ (as shown above). What is the ratio $\ell:w$ in simplified form?

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ultratalk008 ultratalk008 · Answer 1 · 2022-01-09T16:15:55+01:00

ultratalk008 ultratalk008

09-01-2022

Answer:

can you show a picture or a more simplified version?

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anuksha0456 anuksha0456 · Answer 2 · 2022-07-20T23:30:38+02:00

The ratio of the length and the width of the bigger rectangle, l:w = 6:5.

What are ratios?

The ratio is the relational representation of two familiar quantities.

The ratio of two quantities a and b is written as a:b, read as "a is to b", and functions as a/b.

How to solve the question?

In the question, we are asked to determine the ratio l:w, given that each of the smaller rectangles is congruent to each other.

We assume the length of each smaller rectangle to be x, and its width to be w.

Now, from the diagram, we can say that 3x = 4y, as the length of the bigger rectangle is covered by 3 lengths of smaller rectangles or 4 widths of the smaller rectangles.

From this, we can say that x = (4/3)y.

Now, the length of the bigger rectangle l covers 3 lengths of the smaller rectangles.

So, we can say that l = 3x.

Also, the width of the bigger rectangle w covers 2 widths and 1 length of the smaller rectangles.

So, we can say that w = 2y + x.

Thus, the ratio l:w = l/w, can be written as:

3x/(2y + x).

Substituting x = (4/3)y, we get:

= 3(4/3)y/(2y + (4/3)y)

= 4y/((10/3)y)

= 12/10 = 6/5 = 6:5.

Thus, the ratio of the length and the width of the bigger rectangle, l:w = 6:5.

The provided question is inappropriate.

The correct question is:

"Ten boxes are packed tightly in a crate. From above, the packed crate looks like the attachment provided.

The visible faces of the boxes are all congruent rectangles (that means the ten small rectangles in the diagram are the same shape and size). The top of the crate is l inches long by w inches wide, where l ≥ w (as shown above). What is the ratio l:w in simplified form?"

Learn more about ratios at

https://brainly.com/question/2784798

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