Question

PLZZZ I'M DESPERATE!!! I GIVE FIVE STARS AND BRAINLIEST!!!! PLZZZZ ASAP! Ten boxes are packed tightly in a crate. From above, the packed crate looks like this. 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?

Answer 1

Answer:

$6:5$

Step-by-step explanation:

Let $a$ be the length of the longer side of the smaller rectangle and $b$ be the length of the shorter side of the smaller rectangle

When you look at the combined rectangle from top to bottom, you can see that $3a=l$. Therefore, $a=\frac{1}{3}l$

This is the same for $4b=l$. Thus, $b=\frac{1}{4}l$

When you look from right to left, you can see that $w = 2b+a$. Using this, we can represent $w$ in terms of $l$.

$w=\frac{1}{2}l+\frac{1}{3}l\\\\w=\frac{5}{6}l$

Now, we can find the ratio of $l:w$:

$l:\frac{5}{6}l\\\\1:\frac{5}{6}\\\\6:5$

This question was quite hard to explain.

If you have any questions about the solution, feel free to ask.

Please have a look at the diagram below to get a better understanding of the solution.