The perimeter of a rectangle is equal to 24
. if the length is halved and the width is tripled, the new perimeter is increased by 8
. what is the length of the original rectangle?

The length of the original rectangle is 8.

Step-by-step explanation:

If we call w the width and call L the length of the rectangle then the perimeter is calculated by the following equation:

In this case we know that the perimeter P is: P=24

Then:

If we call the new width of the rectangle w 'then

If we call the new length of the rectangle L 'then

Therefore:

Now solve we have the following system of equations

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To solve the system multiply the first equation by -3 and add it to the second equation

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

they go with it happens or they mite give a chance?

step-by-step explanation: