Draw a rectangle that is twice as wide as it is tall, and that fits snugly into the triangular region formed by the line 3x + 4y = 12 and the positive coordinate axes, with one corner at the origin and the opposite corner on the line. Find the dimensions of this rectangle.

Question

calculusxy · Answer

@mathstudent55 @agent0smith

calculusxy · Answer

I usually have some difficulty understand when it says "twice as wide as it is tall," but I put the width to be x and the height to be 2x.

calculusxy · Answer

Is that correct?

agent0smith · Answer

"twice as wide as it is tall," means if the height is x, width is 2x

calculusxy · Answer

Okay. So 3x would be the width and the 4y would be the height right?

calculusxy · Answer

Like can I do 3(2x) + 4(x) = 12?

agent0smith · Answer

You should be using a diagram btw...

The point on the line is (x, y), or (2x, x)

Plug them into the equation 3x + 4y = 12 and solve for x, then find y.

agent0smith · Answer

Exactly.

calculusxy · Answer

6x + 4x = 12 
10x = 12
x = 6/5

calculusxy · Answer

Width: 6/5 x 2 = 12/5 units
Height: 6/5

calculusxy · Answer

Is that right?

agent0smith · Answer

Yep. A diagram would help confirm it though.

calculusxy · Answer

OK.

calculusxy · Answer

Can you help me with a couple more questions?

agent0smith · Answer

Okay

calculusxy · Answer

I made a new post and mentioned you too