A 10m by 20m pool is to be surrounded by a deck of uniform width. The area of the deck is twice the area of the pool, what is the width of the deck?
Pool A=10 x 20 = 200
Deck A=200(2)=400
Total Area=400+200=600
(10+x)(20+x)=600
200+10x+20x+4x^2=600
4x^2+30x-400=0
did quadratic equation, got 10 or -20
Added 10 to length & width
20 x 30 =600, which is the total area. Therefore the deck is 20 x 30, would 20 be the width. IS THIS CORRECT?
Is this right?
x is the total amount added. Since you get x=10, that means that 5m was added on each side.
I'm interested in how you made this calculation:
(10+x)(20+x)=600
200+10x+20x+4x^2=600
Where did the 4x^2 come from? looks like answer analysis to me. In addition, you did not solve that equation, or you would not have come up with the answer. Looks like you figured it out by inspection and then tried waving your hands to posit a reasonable-looking equation.
The proper equation, since the amount added was x on each side, or 2x total, is
(10+2x)(20+2x) = 600
200+60x+4x^2 = 600
or, dividing by 4,
x^2+15x+50 = 150
x^2+15x-100 = 0
(x+20)(x-5) = 0
x = 5
So, the amount added all around is 5m, making the total area
20x30 = 600 m^2
Doing it your way, with x as the total added, you should have had
x^2+30x-400 = 0
(x-10)(x+40) = 0
x = 10 or -40
With x=10, that's 5 on each side.
I tried this question two ways,
(10x+2x)(20x+2x)-did quadratic equation instead of factoring & got incorrect answer so I did (10+x)(20+x)with quadratic equation & got 5 or -20, chose 5 & sub'ed into area to check but when typing in here I typed the 4x^2 from my formula in my first attempt into the 2nd attempt equation instead of x^2, that is where I got mixed up, otherwise I did get x=5 on paper. Had not did drawing, so forgot to add to each side of the width & length. I can see where I went wrong,I was on the right track. Thank you for clarifying,
To find the width of the deck, we need to set up an equation using the given information. Let's call the width of the deck "x".
Given that the pool has dimensions of 10m by 20m, its area can be calculated by multiplying the length and width: 10m * 20m = 200m².
The area of the deck is twice the area of the pool, so we can write the equation: deck area = 2 * pool area.
Let's calculate the deck area first. The outer dimensions of the deck will be 10m + 2x (adding x on both sides of the pool) and 20m + 2x (adding x on both ends of the pool).
Deck area = (10m + 2x) * (20m + 2x)
Now we can set up the equation:
(10m + 2x) * (20m + 2x) = 2 * 200m²
Expanding and simplifying the equation:
(10m * 20m) + (10m * 2x) + (20m * 2x) + (2x * 2x) = 400m²
200m + 20mx + 40mx + 4x² = 400m²
Combine like terms:
4x² + 60mx + 200m - 400m² = 0
Now we have a quadratic equation in the form of ax² + bx + c = 0, where a = 4, b = 60m, and c = 200m - 400m².
To solve this equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Let's substitute the values into the formula:
x = (-(60m) ± √((60m)² - 4(4)(200m - 400m²))) / (2(4))
Simplifying further:
x = (-60m ± √(3600m² - 16(200m - 400m²))) / (8)
Now we can calculate the two possible values for x.