Respuesta :
The width is 5 meters.
Let w = the width of the gardens. In the first garden, the length is twice the width, so l = 2w.
In the second garden, the length is 4 more than the first garden, so l = 2w+4.
The area of a rectangle is found by multiplying the length and width; for the second garden, that is
w(2w+4) = 70
Using the distributive property,
w*2w+w*4 = 70
2w² + 4w = 70
We can factor a 2 out of the left hand side:
2(w² + 2w) = 70
Divide both sides by 2, and we have
w² + 2w = 35
We want the equation equal to 0 to find the roots (solutions), so subtract 35 from both sides:
w² + 2w - 35 = 35 - 35
w² + 2w - 35 = 0
This is easily factorable; we want factors of -35 that sum to 2. 7(-5) = -35 and 7 + (-5) = 2, so
(w+7)(w-5) = 0
Using the zero product property, we know that either w+7=0 or w-5=0; this gives us w=-7 or w=5. Since a negative width makes no sense, we know that w=5.
Let w = the width of the gardens. In the first garden, the length is twice the width, so l = 2w.
In the second garden, the length is 4 more than the first garden, so l = 2w+4.
The area of a rectangle is found by multiplying the length and width; for the second garden, that is
w(2w+4) = 70
Using the distributive property,
w*2w+w*4 = 70
2w² + 4w = 70
We can factor a 2 out of the left hand side:
2(w² + 2w) = 70
Divide both sides by 2, and we have
w² + 2w = 35
We want the equation equal to 0 to find the roots (solutions), so subtract 35 from both sides:
w² + 2w - 35 = 35 - 35
w² + 2w - 35 = 0
This is easily factorable; we want factors of -35 that sum to 2. 7(-5) = -35 and 7 + (-5) = 2, so
(w+7)(w-5) = 0
Using the zero product property, we know that either w+7=0 or w-5=0; this gives us w=-7 or w=5. Since a negative width makes no sense, we know that w=5.
Answer:12
Step-by-step explanation:
DONT LISTEN TO THE GUY ON TOP I TOOK THE TEST>:(
