The length of a rectangle is three times as long as the width. If each side is increased by 6, the area of the new rectangle is 156 more than the area of the original rectangle. What are the...

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The length of a rectangle is three times as long as the width. If each side is increased by 6, the area of the new rectangle is 156 more than the area of the original rectangle. What are the dimensions of the new rectangle?

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Since length of rectangle is three times as long as the width we have

`a=3b`                                                                       (1)

Also, if we increase each side by 6 (new sides are `a+6` and `b+6` ) the area of rectangle increases by 156 and since the area of rectangle is equal to product of it' two sides we get

`(a+6)(b+6)=ab+156`                                           (2)

Now we use (1) to replace `a` with `3b` in (2).

`(3b+6)(b+6)=3b cdot b+156`

`3b^2+18b+6b+36=3b^2+156`

`24b=120`

`b=5`

Now from (1) we get

`a=15`

So dimensions of old rectangle are `a=15` and `b=5` and since new rectangle has each side longer by 6 the new dimensions are `a=21` and `b=11.`

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