a four sided garden plot has an irregular shape. the second side is 12 feet longer than the first. the third side is 24 feet longer than the second. the fourth side is 36 feet longer than the third. if the perimeter of the plot measures 136 feet, what is the length of the longest side?
The sides are
a
b=a+12
c=b+24
d=c+36
So,
a+b+c+d = 136
a+b+c+c+36 = 136
a+b+2c = 100
a+b+2(b+24) = 100
a+b+2b+48 = 100
a+3b = 52
a+3(a+12) = 52
4a+36 = 52
4a = 16
a = 4
So, the sides are 4,16,40,76
Thank you very much Steve.
If a triangle has side lengths of 11 cm, 12 cm, and x cm, find the range of possible values of x.
To find the length of the longest side of the four-sided garden plot, we need to determine the lengths of all four sides first. Let's start with the information given:
Let x be the length of the first side.
According to the problem, the second side is 12 feet longer than the first side, so its length is x + 12.
The third side is 24 feet longer than the second side, so its length is (x + 12) + 24 = x + 36.
Similarly, the fourth side is 36 feet longer than the third side, so its length is (x + 36) + 36 = x + 72.
Now, we can write the equation for the perimeter:
Perimeter = length of the first side + length of the second side + length of the third side + length of the fourth side.
Since the perimeter is given to be 136 feet, we can write:
136 = x + (x + 12) + (x + 36) + (x + 72).
Now let's solve the equation:
136 = 4x + 120.
Subtracting 120 from both sides:
16 = 4x.
Dividing both sides by 4:
x = 4.
So, the length of the first side is 4 feet.
To find the longest side, we substitute x = 4 into the equation for the fourth side:
Length of the fourth side = x + 72 = 4 + 72 = 76 feet.
Therefore, the longest side of the four-sided garden plot measures 76 feet.