P = L + L + w + w
72 = 2(L) + 2(L-4)
Distribute
72 = 2(L) + 2(L) - 8
Add like terms
72 = 4(L) - 8
Subtract 8 from both sides
64 = 4(L)
Divide both sides by 4
16 = L
The length is 16. Now substitute that in the equation for finding w.
w = L - 4
w =
A fraction that is equivalent to 1/4 is 25/100
Answer:
12, 13, 14
Step-by-step explanation:
Denote the integers as:
x
x+1
x+2
The sum of their squares, so that would be;
(x^(2)) + (( x + 1 )^(2)) + (( x + 2 )^(2)) = 509
write out the squares
x^2 + x^2 + 2x + 1 + x^2 + 4x + 4 = 509
combine like terms
3x^2 + 6x + 5 = 509
inverse operations
3x^2 + 6x + 5 = 509
-5 -5
3x^2 + 6x = 504
factor
3x^2 + 6x = 504
3 ( x^2 + 2x ) =504
Inverse operations
3 ( x^2 + 2x ) = 504
/3 /3
x^2 + 2x = 168
Factor again
x ( x + 2 ) = 168
At this point, it should be obvious that x is 12 (because 12 * 14 = 168)
So now substitute back into the consecutive numbers
x = 12
x + 1 = 13
x + 2 = 14
A^2 + b^2 = c^2 a=4 b= 6
4^2 + 6^2 =52
square root that:
c=2 square root 13 exactly or 7.2 approximately <span />
