LM is the midsegment of trapezoid ABCD. AB= x + 8, LM = 4x + 3, and DC = 187. What is the value of x?
Since LM is the midsegment of trapezoid ABCD, it divides the trapezoid into two congruent triangles. This means that the length of LM is equal to half the sum of the lengths of the bases of the trapezoid.
In this case, the length of LM is given as 4x + 3, and the length of DC is given as 187. Let's represent the length of AB as y.
Since LM is half the sum of the lengths of the bases, we have: 4x + 3 = (y + 187)/2
Similarly, the length of AB is given as x + 8, so we have: y = x + 8
Now we can substitute the value of y in the equation for LM:
4x + 3 = ((x + 8) + 187)/2
Multiplying both sides of the equation by 2 to eliminate the fraction gives:
8x + 6 = x + 195
Subtracting x from both sides of the equation gives:
7x + 6 = 195
Subtracting 6 from both sides of the equation gives:
7x = 189
Dividing both sides of the equation by 7 gives:
x = 27
Therefore, the value of x is 27.