Question

Cynthia Bech want to buy a rug for a room that i 20 ft wide and ft long. She want to leave a uniform trip of 29 floor around the rug. She can afford to buy 322 quare feet of carpeting. What dimenion hould the rug​ have?

Answer 1

On solving the question, we got that - The dimensions of the rug should be 18 feet and 24 feet

What is area of rectangle?

By multiplying the rectangle's length by its breadth, we may get its area.

Equiangular quadrilaterals, like rectangles, are known in this way. This is so because a rectangle is a four-sided quadrilateral shape with parallel sides that are equal to one another and four corners with 90o angles. Rectangles are sometimes known as equiangular quadrilaterals since all of its angles are 90 degrees.

the parameters provided;

The room is 20 feet by 26 feet in size.

432 feet2 is the largest area rug she can afford.

If the floor will be a uniform stripe around the rug, then each dimension should have its uniform extra length of floor =  (y).

$Area = Length X Width\\432 = ((20=y) X (26-y)\\432 = 520 - 20y - 26y + y^2\\y^2 - 46y+88=0$

here, a= 1, b= -46, c =88

$y = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a}$

$y = \frac{-(-46) +/- \sqrt{(-46)^2 - 4X1X88} } {2} \\\\y = 44 \\or\\ y = 2$

Therefore, Length = 20-2 = 18 ft

and width = 26-2 = 24ft

To know more about rectangle visit:

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