Final answer:
To find the value of x, we can use the fact that triangle LMN is congruent to triangle GRS. By applying the properties of congruent triangles, we can determine that the value of x is equal to the length of one side of triangle LM or GR.
Step-by-step explanation:
To find the value of x, we need to use the fact that triangle LMN is congruent to triangle GRS. This means that the corresponding sides and angles of the two triangles are equal. Let's denote the length of side LM as a and the length of side GR as b.
From the given information in the question, we can see that AC is equal to 3 times the length of side GR, so AC = 3b. Using similar logic, we can conclude that AB is equal to 3 times the length of side LM, so AB = 3a.
Since the width of the Moon as seen from point H is KD = x, which is equal to the length of side LM, we can substitute KD = x into the equation AB = 3a and solve for x. Therefore, the value of x is x = AB/3 = (3a)/3 = a.