Answer:
10m x 15m
Step-by-step explanation:
You are given some information.
1. The area of the garden: A₁ = 150m²
2. The area of the path: A₂ = 186m²
3. The width of the path: 3m
If the garden has width w and length l, the area of the garden is:
(1) A₁ = l * w
The area of the path is given by:
(2) A₂ = 3l + 3l + 3w + 3w + 4*3*3 = 6l + 6w + 36
Multiplying (2) with l gives:
(3) A₂l = 6l² + 6lw + 36l
Replacing l*w in (3) with A₁ from (1):
(4) A₂l = 6l² + 6A₁ + 36l
Combining:
(5) 6l² + (36 - A₂)l +6A₁ = 0
Simplifying:
(6) l² - 25l + 150 = 0
This equation can be factored:
(7) (l - 10)*(l - 15) = 0
Solving for l we get 2 solutions:
l₁ = 10, l₂ = 15
Using (1) to find w:
w₁ = 15, w₂ = 10
The two solutions are equivalent. The garden has dimensions 10m and 15m.
Answer: Your brother is 15 years old right now.
Step-by-step explanation:
Let be "m" your currently age and "b" your brother's currently age.
Knowing that right now he is three times (this indicates multiplication) as old as you, you can write the following equation:
In five years your age will be:
And your brother's age will be:
Then, if in five years, your brother will be twice as old as you, you can set up the second equation:
Then, the System of equations is:
Apply the Substitution method and substitute the first equation into the second one and solve for "m":
Substitute the value of "m" into the first equation and evaluate in order to find "b":
So remember that the pythagorean theorem is a^2+b^2=c^2
c=18
legnth is 3 more than width
l=3+w
a=3+b
subsitute
(3+b)^2+b^2=18^2
expand
9+6b+b^2+b^2=324
subbtract 9 from both sides
6b+2b^2=313
subtract 313 from both sides
2b^2+6b-313=0
factor
use quadratic formula and get
b=11.1
subsitute
a=3+b
a=3+11.1
a=14.1
answer is 14.1 ft by 11.1 ft
