Answer: X = 5 and Y = 6
Step-by-step explanation: The rectangle IJKL has dimensions for both lengths and both widths. JK and IL are the lengths and are given as 3X + 21 and 6Y. Also JI and KL are the widths and are given as 6Y - 6 and 2X + 20. Note that in any rectangle, the lengths are always equal to each other, and the same goes for both widths. Hence what we can conclude from that is
3X + 21 = 6Y and
6Y - 6 = 2X + 20
By simplifying further and collecting like terms we now have
3X - 6Y = -21 ——————(1)
6Y - 2X = 26 ——————(2)
What we now have is a pair of simultaneous equations. In order to solve for X and Y, we shall use the elimination method because all the unknown variables have a coefficients greater than 1. In order to eliminate the X variable, we shall multiply all through with the coefficients of X. So we multiply equation (1) by -2 and we multiply equation (2) by 3. Now we have,
3X - 6Y = -21 —— (x -2)
6Y - 2X = 26 ——-(x 3)
We now have a new set of simultaneous equations
-6X + 12Y = 42 ————(3)
18Y - 6X = 78 ————--(4)
Now we subtract equation (3) from equation (4) and that gives us
6Y + 0 = 36
6Y = 36
Divide both sides of the equation by 6
Y = 6
Now we can substitute the value of Y in equation (1)
3X - 6(6) = -21
3X -36 = -21
Add 36 to both sides of the equation
3X = 15
(Note that -36 + 36 = 0 and -21 + 36 = 15)
3X = 15
Divide both sides of the equation by 3
X = 5.
If you substitute for the values of X and Y in all four sides of the rectangle then you’ll have
Length = 36 and
Width = 30
