Question

Quadrilateral HIJK is a rectangle, and it's given that HJ = 13w + 26 and IK = w + 50. What is the value of w?

Answer 1

To determine the value of w, set the sides equal (13w + 26 = w + 50), subtract w and 26 from both sides, and then divide by 12 to get w = 2.

Step-by-step explanation:

The student is asked to solve for the variable w given that HIJK is a rectangle with sides HJ and IK, and it's provided that HJ = 13w + 26 and IK = w + 50. In a rectangle, opposite sides are equal in length, so HJ = IK.

To find the value of w, we set the two expressions equal to each other and solve for w:

1. 13w + 26 = w + 50
2. 12w = 24 (by subtracting w and 26 from both sides)
3. w = 2 (by dividing both sides by 12)

Therefore, the value of w is 2.