Suppose ABCD is a parallelogram. If AB=9x+2, CD=12x−4, BC=x+7,determine the length of ¯¯¯¯¯¯¯¯¯AD???

Step-by-step explanation:

Given

ABCD is a parallelogram with

In a parallelogram, opposite sides are equal and parallel

Therefore, the length of AD is equal to BC i.e.  

Also,

on solving

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions