1. A square of side length X +1 has an area of 6 square units. Find the units of X to the nearest hundreth

2. Is it possible to design a building so that the rectangular ground floor has a perimeter of 50 and an area of 160m ^2? Explain

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Posted by Admin in Saturday, February 5th 2011 3 comments already

1. A square of side length X +1 has an area of 6 square units. Find the units of X to the nearest hundreth

2. Is it possible to design a building so that the rectangular ground floor has a perimeter of 50 and an area of 160m ^2? Explain

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jrrymiller Said,

February 5th, 2011 @9:51 pm

Whoops. SnizzleD made a mistake x+y=25 not fifty.

a building 46 by 3 does not have a perimeter of 50

It is the correct technique though.

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1. How do you find the area of a square? Multiply the side length by itself. So, the side length is x+1. And the area is 6. So:

(x+1)(x+1) = 6

x^2 + 2x + 2 = 6

Put this in quadratic form:

x^2 + 2x – 4 = 0

Solve using quadratic formula

x = 1.2361, -3.2361

Obviously the side length is not negative, so the answer is 1.2361.

2. Let x=length of building, y=width of building.

x+y = 50 (perimeter)

x*y = 160 (area)

Substitute:

x+y=50

y=50-x

xy=160

x(50-x)=160

50x – x^2 = 160

-x^2 + 50x – 160 = 0

Solve for x using quadratic equation:

x = 3.4361, 46.5644

Looks like there might be two solutions to this problem. Let’s find y in both cases:

xy=160

3.4361y=160

y=46.5644

xy=160

46.5644y=160

y = 3.4361

So, the answer is yes, you can design a building with a perimeter of 50 and area of 160. The dimensions of the base would have to be 3.4361 x 46.5644.