A rectangle garden is 10 feet by 16 feet. When each dimension is increased by the same amount, the area is increased by 40 square feet. If x represents the number of feet by which each dimension is increased, which equation could be used to find the correct value for x?
a) 21x^2+21x-20=0
b) x^2+26x-40=0
c) x^2-26x-40=0
d) x^2-26x+120=0
2007-05-28 18:03:14 · 11 answers · asked by jamie68117 3 in Science & Mathematics ➔ Mathematics
(10+x)(16+x) = 160 + 40
160 + 26x + x^2 = 160 +40
x^2 + 26x - 40 = 0
(b)
2007-05-28 18:07:51 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Ok so.. to work out this you want to start with what you know.
So we know that the width is 10 feet and the length is 16 feet.
So we can write that as W = 10 and L = 16
We also that the area is L x W = A
so 10 x 16 = 160
From the question we are told that each dimension is increased by the same amount and that the area (ie. A) is increased by 40 sq feet.
x - number of feet by which each dimension is increased.
So from this we can see that the length is increased by x feet and the width is increased by x ft
Therefore W = 10 + x L = 16 + x
The area is increased by 40 so
the area (A) now equals 160 + 40
Therefore:
(10+x)(16+x) = 160 + 40
Expanding the brackets we get:
160 + 10x + 16x + x^2 = 200
160 + 26x + x^2 = 200
x^2 + 26x - 40 = 0
We can see that this eqn is the same as b) and therefore our answer is b)
Hope this helps =]
2007-05-29 01:23:35 · answer #2 · answered by Anonymous · 0⤊ 0⤋
The original area of the garden was 160 sqft
after increase,the area would be
(10+x)(16+x)=160+26x+x^2
Therefore x^2+26x+160=160+40
=>x^2+26x-40=0
Hence equation b should be used to find the value of x
2007-05-29 01:15:22 · answer #3 · answered by alpha 7 · 0⤊ 0⤋
Answer is b.
each dimension is increased by the same amount:
10 + x, 16 + x
Area is increased by 40
(10*16) + 40 = 160 + 40(don't add yet)
A = l*w
160 + 40 = (10 + x)(16 + x)
160 + 40 = 160 + 26x + x^2 ...then remove 160
40 = x^2 + 26x
0 = x^2 + 26x - 40 (or the other way around!)
that's it.
2007-05-29 01:16:40 · answer #4 · answered by megavinx 4 · 0⤊ 0⤋
The second one: (16+x)*(10+x)=160+40 => 16x+x^2+160+10x=160+40 => x^2+26x-40=0
2007-05-29 01:11:00 · answer #5 · answered by ArArAt 3 · 0⤊ 0⤋
The initial area is 10*16 = 160 square feet. Increasing the length and width by some amount "x" would mean the new area is (10+x) * (16+x). This is 40 more than the original area, so it's 160+40 = 200 square feet.
Take (10+x)(16+x) = 200 and simplify.
2007-05-29 01:10:48 · answer #6 · answered by Anonymous · 0⤊ 0⤋
W = 10ft
L = 16ft
A0 = 10*16 = 160ft^2
(10 + x)*(16+x) = 200ft^2
160 + 26x + x^2 = 200
x^2 + 26x - 40 = 0
The answer is (b)
2007-05-29 01:09:45 · answer #7 · answered by mark r 4 · 0⤊ 0⤋
b) x^2+26x-40=0
2007-05-29 06:00:13 · answer #8 · answered by Sumita T 3 · 0⤊ 0⤋
(x+10)(x+16) = 160 + 40
X^2 + 26X - 40 = 0
b)
Only the positive answer is valid.
2007-05-29 01:12:11 · answer #9 · answered by kooseh 1 · 0⤊ 0⤋
b
2007-05-29 01:09:18 · answer #10 · answered by na 2 · 0⤊ 0⤋