Jose needs to enclose a rectangular section of his yard. The area is 35 sq. ft. and the perimeter is 27 sq. ft. Find the length and width of the section.
let l be the length, and w be the width in feet.
so 2l+2w=27 --->l+w=13.5 ----> w=13.5-l
secondly lw=35
l(13.5-l)=35
expand and express as a quadratic equation, you will have to use the formula
Let me know what you get.
kj,hjhd
To solve the quadratic equation, we'll use the quadratic formula:
For a quadratic equation in the form of ax^2 + bx + c = 0, the formula is:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, our quadratic equation is l(13.5 - l) = 35, which can be rewritten as l^2 - 13.5l + 35 = 0.
Comparing this to the general form ax^2 + bx + c = 0, we have:
a = 1, b = -13.5, and c = 35.
Now, let's substitute these values into the quadratic formula:
l = [ -(-13.5) ± sqrt((-13.5)^2 - 4(1)(35)) ] / (2*1)
Simplifying this equation, we get:
l = [ 13.5 ± sqrt(182.25 - 140) ] / 2
l = [ 13.5 ± sqrt(42.25) ] / 2
Taking the square root of 42.25, we have two possibilities:
l = [ 13.5 ± 6.5 ] / 2
Case 1: When l = [ 13.5 + 6.5 ] / 2
l = (20) / 2
l = 10
Case 2: When l = [ 13.5 - 6.5 ] / 2
l = (7) / 2
l = 3.5
Therefore, we have two possible values for the length: l = 10 feet or l = 3.5 feet.
Now that we have the length, we can find the width by using the equation w = 13.5 - l.
Case 1: For l = 10 feet,
w = 13.5 - 10
w = 3.5 feet
Case 2: For l = 3.5 feet,
w = 13.5 - 3.5
w = 10 feet
So, the two possible sets of length and width values for the rectangular section are:
(10 feet, 3.5 feet) and (3.5 feet, 10 feet).