A rectangular garden that measures 25 X 50 ft is increased on all sides by the same amount. Its area increased by 400 square feet. What was th increase in each dimension?
Show work and expain please.
2007-04-03 12:33:09 · 8 answers · asked by Katey 1 in Science & Mathematics ➔ Mathematics
Call the "same amount" x.
(x+25)(x+50)= 1250+400 (since 1250= 25*50)
x^2 + 75x + 1250 = 1650
x^2 + 75x - 400= 0
(x+80)(x-5 )= 0
So x= 5 since it can't be -80!!!
Good luck!!!
2007-04-03 12:40:55 · answer #1 · answered by kash 3 · 0⤊ 0⤋
If the sides were increased by a distance of x, then the new dimensions are (25+2x) and (50+2x). The product of this should be the the old area plus 400 square feet. So:
(25+2x)(50+2x) = (25)(50) + 400
25(50) + 100x + 50x + 4x^2 = (25)(50) + 400
4x^2 + 150x - 400 = 0
Using the quadradic forumula, you get:
x = [ -150 ±â(150² - 4(4)(-400)) ] / 2(4)
x = [ -150 + â(150² + 6400) ] / 8 (we can get rid of the negative solution, because negative feet doesn't make any sense)
x = [ -150 + â(28,900) ] / 8
x = [ -150 + 10â(289) ] / 8
x = [ -150 + 10(17) ] / 8
x = 20./ 8
x = 5/2, so the garden was stretched two and a half feet in each of the 4 directions, increasing the length by 5 feet and the width by 5 feet.
2007-04-03 19:51:59 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Let the increase in each dimension be x ft.
Then (25 + x)(50 + x) = 1250 + 400
1250 + 75x + x^2 = 1250 + 400
x^2 + 75x - 400 = 0
(x + 80)(x - 5) = 0
Discarding the negative root,
x = 5ft.
Check: 25x50 = 1250, 30x55 = 1650, 1650 - 1250 = 400ft^2.
2007-04-03 19:49:01 · answer #3 · answered by Anonymous · 0⤊ 0⤋
A = WL
A = 25 * 50
A = 1250
1250 + 400 = (20+x)(25+x)
1650 = 1250 + 20x + 25x + x^2
x^2 + 75x - 400 = 0
(x-5)(x+80)
x = 5
so the dementions are increased by 5
2007-04-03 19:44:09 · answer #4 · answered by 7 · 0⤊ 0⤋
The original area is 25*50=1250 ft^2 so the new area is, therefore, 1650 ft^2. Set it up this way: (25+x)(50+x)=1650 and solve.
2007-04-03 19:41:12 · answer #5 · answered by bruinfan 7 · 0⤊ 0⤋
(25+x)(50+x) = 25*50+400
1250 + 75x + x^2 = 1650
x^2+75x -400 =0
(x+80)(x-5) = 0
x=5 feet
2007-04-03 19:45:02 · answer #6 · answered by ironduke8159 7 · 0⤊ 0⤋
25*50=1250
(25+x)*(50+x)=1650
1250+75x+x^2 = 1650
x^2+75X-400=0
(-75-+sqrt(75^2+1600))/2=
(-75+85)/2 = 5
(-75-85)/2=-80
So 5 will be the answer
2007-04-03 19:47:57 · answer #7 · answered by eyal b 4 · 0⤊ 0⤋
This is clearly a homework question and it servers no one’s interests, including yours, to answer it for you. But I will help you with some direction.
You use the equation that relates the area of the rectangle to its two side. This equation is Area=Side1XSide2
Now let
Side1=side1Before + amount
And
Side2=side2before + amount
substitute and solve.
2007-04-03 20:19:53 · answer #8 · answered by David Dodeca 5 · 0⤊ 0⤋