Answer:
Option (a).
Step-by-step explanation:
1) Pedro decided to build a rectangular enclosure with an area of 36 m². How many meters of canvas will he have to buy to make the enclosure considering that one side will be 3 meters more than the other?
Let the length of the rectangle be x then the width will be (3+x) m
The area of a rectangular enclosure is 36 m².
To find how may meter of canvas will he have to buy to make the enclosure, we can find its perimeter. Firstly finding length and breadth using formula of area of rectangle.
[tex]A=l\times b\\\\36=x(x+3)\\\\x^2+3x-36=0[/tex]
[tex]x=\dfrac{-3+\sqrt{3^{2}-4(1)(-36)}}{2\times(1)},\dfrac{-3-\sqrt{3^{2}-4(1)(-36)}}{2\times(1)}\\\\x=4.68\ m\ \text{and}\ -7.68\ m[/tex]
Neglecting negative value, we get the length is 4.64 m
Width, b = (3+x) = (3+4.64) = 7.64 m
The perimeter of rectangle is :
P = 2(l+b)
P = 2(4.64 m+7.64 m)
P = 24.56 m
or
P = 25 m
Hence, 25 m of canvas will he have to buy to make the enclosure.
