Answer: the value of k is 3
Step-by-step explanation:
Triangle DEF is similar to triangle PQR. This means that the ratio of the length of each side of ∆DEF to the length of the corresponding side of ∆ PQR is constant. Therefore,
DE/PQ = EF/QR = DF/PR
Therefore,
24/12 = 6/k
Cross multiplying, it becomes
k × 24 = 12 × 6
24k = 72
Dividing the left hand side and the right hand side of the equation by 24, it becomes
24k/24 = 72/24
k = 3
