A rectangle garden measures 15m by 24m. A larger garden is to be made by increasing each side 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 metre.
Redid the quadratic equation, got 4.16 or -43.16
Rounded 4.16 to 4.2 Sub'ed into dimensions
15+4.2=19.2 & 24+4.2=28.2
19.2 x 28.2 =541.44, close to 540
IS THIS CORRECT?
A=15 x 24=360 existing garden
A=360 x 1.5=540
W=15+2x L= 24+2x
(15+2x)(24+2x)= 540
4x*2+78x-180=0
x=-78+or- square root of 78*2-4(4)(-180)/2(4)
=-78+or - sq root 6084 +2880/8
=89 or 66
OR
540=15(1.5)x 24(1.5)
= 22.5 x 36=810 not correct??
please reply
(15+x)(24+x)= (15*24)(1.5)
360+15x+24x+x^2=540
x^2+39x-180=0
cannot factor?
tried quadratic equation, got x=+/-15.33??
Yes it is correct but how come we don’t put 2x?
To find the dimensions of the new garden, we first need to calculate its area.
The area of the original garden is given by the formula: Area = length × width.
For the original garden, its length is 15m and width is 24m.
So, the original area of the garden = 15m × 24m = 360m².
Now, let's assume that we increase both the length and width of the garden by the same amount, denoted as "x". The new length becomes 15m + x, and the new width becomes 24m + x.
The area of the new garden is given by the formula: New Area = (Length + x) × (Width + x).
According to the problem, the new area is to be 1.5 times the original area. So, we can write the equation:
1.5 × Original Area = (Length + x) × (Width + x).
Substituting the values, we get:
1.5 × 360m² = (15m + x) × (24m + x).
Now, let's solve this equation to find the value of "x."
1.5 × 360m² = (15m + x) × (24m + x).
540m² = 360m² + 15x + 24x + x².
Combining like terms and rearranging, we have:
x² + 39x - 180m² = 0.
To solve this quadratic equation, we can either factor it or use the quadratic formula.
By factoring, we find:
(x + 15)(x - 12) = 0.
So, x = -15 or x = 12.
Since the dimensions of the garden cannot be negative, we discard x = -15.
Therefore, the value of x is 12.
Now, let's find the new dimensions of the garden:
New length = 15m + x = 15m + 12m = 27m.
New width = 24m + x = 24m + 12m = 36m.
Therefore, the dimensions of the new garden are approximately 27m by 36m (to the nearest tenth of a meter).
(15+x)(24+x)=(15*24)(1.5)
This should help.