shaquana has a deck that measures 18 feet by 15 feet. She wants to increase each dimension by equal lengths so that its area tri

Question

2 years ago

11

ples. How much should each dimension increase?

1 answer:

Svetach [21] · Answer 1 · 2023-10-05T08:06:04+03:00

to increase each dimension by equal lengths so that its area triples is 12 feet.

The given dimensions are 18 feet by 15 feet.

We need to find how much should each dimension increase.

Shaquana wants to increase each dimension by equal lengths so that its area triples.

Let the increased length be x.

So, length =18+x feet and width=15+x feet.

As we know, the area of a deck=Length×Width

The original area of a deck=18×15=270 square feet.

Now, the new area of a deck=(18+x )×(15+x)=3×270

⇒270+15x+18x+x²=810 square feet

⇒x²+33x-540=0

Here, a=1, b=33 and c=-540 in $x=\frac{-b\±\sqrt{b^{2-4ac} } }{2a}$ .

⇒ $x=\frac{-33\±\sqrt{33^{2} -4 \times (-540)} }{2 \times 1}$

⇒ $x=\frac{-33\±\sqrt{1089 +2160} }{2 \times 1}=\frac{-33\±57}{2}$

⇒x=-45 or x=12

Length can not be a negative integer.

Therefore, to increase each dimension by equal lengths so that its area triples is 12 feet.

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