SOLUTION: Solving Problems with Quadratic Equations 19. A rectangular garden measures 15 m by 24 m. A larger garden is to be made by increasing each side length by the same amount. The resu

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Solving Problems with Quadratic Equations 19. A rectangular garden measures 15 m by 24 m. A larger garden is to be made by increasing each side length by the same amount. The resu      Log On


   

Question 198593: Solving Problems with Quadratic Equations
19. A rectangular garden measures 15 m by 24 m. A larger garden is to be made by increasing each side length by the same amount. The resulting area is ti be 1.5 times the original area. Find the dimensions of the new garden, to the nearest tenth of a meter. Include a diagram in your solution.
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Found 2 solutions by arallie, ankor@dixie-net.com:
Answer by arallie(162) About Me  (Show Source):
You can put this solution on YOUR website!
I don't know how to a diagram, sorry. But I do have the solution.
a%5B1%5D=15%2A24 and a%5B2%5D=1.5a%5B1%5D where a%5B1%5D is area of the smaller rectangle and a%5B2%5D is the bigger one. x will be the width added to the initial rectangle.
a%5B2%5D=%2815%2Bx%29%2824%2Bx%29 is the new dimensions of the rectangle.
Solve
a%5B1%5D=15%2A24=360a%5B2%5D=1.5%28360%29=540
Therefore
540=%2815%2Bx%29%2824%2Bx%29
Solve for x
x%5E2%2B39x%2B360=540x%5E2%2B39x-180=0
Quad From
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ when a=1, b=39, c=-180
Therefore
Real solutions:
Root 1: -43.1696007570893
Root 2: 4.16960075708923
Since taking away is the wrong idea, the answer is 4.16960075708923.
4.16960075708923m needs to be added to each side.

Anymore questions feel free to ask me.
Anthony Allie
arallie@gmail.com
http://arallie.webs.com/tutoring.htm

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular garden measures 15 m by 24 m. A larger garden is to be made by
increasing each side length by the same amount. The resulting area is to be 1.5
times the original area. Find the dimensions of the new garden, to the nearest
tenth of a meter. Include a diagram in your solution.
:
Find the the original area: 15 * 24 = 360 sq/m
Find the new area: 1.5 * 360 = 540 sq/m
:
Let x = amt added to each dimension to increase the area to 540 sq/m
:
(x+15)(x+24) = 540
FOIL
x^2 + 24x + 15x + 360 - 540 = 0
:
x^2 + 39x - 180 = 0
Use the quadratic formula to find x: a=1; b=39; c=-180
The positive solution: x ~ 4.17 meters
;
;
Check solution, add 4.2 to each dimension
19.2 * 28.2 = 541 ~ 540