Ashley saved a distance equal to 80% of the length of the shortest side of a rectangular field by cutting across the diagonal of the field instead of along two of the sides. Find the ratio of the length of the shortest side of the field to the length of its longest side.

Question

calculusxy · Answer

@eliesaab

calculusxy · Answer

@Loser66

mathmate · Answer

As in all geometry problems, making a diagram is half the problem solved.
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We know that the diagonal is shorter than (x+kx) by 80% of x.
Can you put this in an equation?

calculusxy · Answer

This is the equation that I got 
$$(\sqrt{a^2+b^2})^2 = (b + 0.2a)^2$$

mathmate · Answer

That looks good!  So a is the shorter side, right?
Can you continue?

calculusxy · Answer

So I then got 0.96a^2 = 0.4ab after some steps

mathmate · Answer

So far so good!  :)  So what would you do next?

calculusxy · Answer

I thought about dividing both sides by 0.4a 
0.24a = b

calculusxy · Answer

I meant 2.4a = b

mathmate · Answer

You're almost there, keep going @calculusxy

calculusxy · Answer

I assumed that the shorter side be a. So do I divide both sides by a? 
2.4 = a/b?

mathmate · Answer

Ouch!  
`Find the ratio of the length of the shortest side of the field to the length of its longest side.`

calculusxy · Answer

That's where I am having trouble--understanding what variable to isolate...

calculusxy · Answer

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