Plane Geometric Figure Problem 3 Solution

This is the solution for the Algebra plane geometric figure problem as asked by an anonymous visitor which read, "catrina and tom want to buy a rug for a room that s 14 by 15 feet. They want to leave an even strip of flooring uncovered around the edges of the room. How wide a strip if they buy a rug with an area of 110 square feet?"

It's easier to picture this.  Draw a rectangle that's almost a square 14 x 15 feet.  Within in draw another such figure but smaller.   The space between that figure and the 14 x 15 figure is x.  Now the smaller square has an area of 110 square feet.  We now have an equation :


(15 -x ) (14 -x ) = 110

210 + x^2 -14x - 15x = 110

x^2 - 29x + 210 = 110

x^2 -29x + 100 = 0

(x - 25)(x - 4) = 0

x = 4 or 25 however using 25 would result in negative dimensions which does not make sense.  So 4 is the answer

Check:  (15 - 4) (14 - 4) = 110  = 11*10 = 110 

Plane Geometric Figure Problem 2 Solution

This is the Plane Geometric Figure Problem 2 Solution which asked "The length of the second side of a triangle is four less than three times the length of the first side. The length of the third side is one more than the length of the first side. If the perimeter of the triangle is 37 feet, what is the length of the first side?"

Since everything is relative to the 1st side make the 1st side x.

The 2nd side is 3x - 4 (4 less than 3 times the length of the 1st side)

and the 3rd side is x + 1 ( 1 more than the length of the 1st side) 

Now all the sides add up to 37 feet so set all this equal to 37.

x + 3x - 4  + x + 1 = 37

5x - 3 = 37

5x = 40 

x = 8

So the 1st side is 8 the 2nd side is 3(8) - 4 or 20 and the 3rd side is 9 .. 8 + 20 + 9 = 37

Plane Geometric Figure Problem 1 Solution

This is the solution to the Plane Geometric Figure Problem 1 which asked you to "find the dimension of a rectangle whose length is 9 less than twice its width if the perimeter is 120 cm."

In a rectangle 2 times the width plus to times the length equals the total perimeter.

Let the width equal x

Then the length is equal to 2x - 9 which means "9 less than twice its width"

Remember 2 times the width plus to times the length equals the perimeter so..

2(x) + 2(2x - 9) = 120
which is..

2x + 4x - 18 = 120

6x - 18 = 120

6x = 120 + 18

6x = 138

x = 138/6

x = 23

Since we let x stand for the width then the width of the rectangle is 23 cm and the length is 2(23) - 9 = 46 - 9 = 37

So the width is 23 cm and the length is 37 cm

Check 2(23) + 2(37) = 120

46 + 74 = 120
120 = 120

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