Answer:
15 and 20 inches
Explanation:
Shown by the picture attached, the rectangle is made up of the sides x and y, where x is the length and y is the width. The perimeter is found by adding all the sides together, so we get the equation:
P=x+y+x+y
P=2x+2y
It is given in the problem that the perimeter is 70 inches, we can substitute this into our equation to get
70=2x+2y
The equation for area can be found by multiplying the length by the width, so we get the equation:
A=xy
It is given in the equation that the area is 300 square inches, so we can substitute this into our equation to get
300=xy
Now we have to equations 70=2x+2y and 300=xy. We can solve for values x and y by using the substitution method (solving for one variable in one equation and plugging it into another)
Let's solve for x in 70=2x+2y
70-2y=2x
35-y=x
x=35-y
We can substitute this back into the equation 300=xy and solve for y
300=(35-y)y
300=35y-y²
0=-y²+35y-300
0=y²-35y+300
0=(y-15)(y-20)
y=15, 20
If we plug these values back into the equation x=35-y or 300=xy, both values work. For both of these equations, we get that x=15, 20.
For our length and width (x,y) we have found two values for each. This is because length and width are essentially interchangeable. A rectangle can be rotated. Taking the picture attached, we could rotate it so that the x is on the bottom, representing the width and y representing the length. These would change the values of our x and y, even though the dimensions would stay the same. Even though we know the dimensions of the tile, we don't need to assign the values to any specific variable as it can change depending on how the rectangle is rotated.
Therefore we know that the dimensions of the tile are 15 and 20.
*keep note that if you set y=15 then x must be 20 and if you set y=20 then x must be 15. You can not say that x and y both equal 15 or both equal 20.