Answer:
2. x = 3
3. x = 10 and y =2
Step-by-step explanation:
2.
From inspection, we can see that EF = 10 and KL = 5
Therefore the ratio KL : EF = 5 : 10 = 5/10 = 1/2
This means that the side measures of ΔJKL are 1/2 the corresponding side measures of ΔGEF
Therefore, if GF = 22, then JL = 22 ÷ 2 = 11
So: 2x + 5 = 11
⇒ 2x = 11 - 5 = 6
⇒ x = 6 ÷ 2 = 3
x = 3
3.
From inspection, we can see that DF = 12 and HJ = 9
Therefore the ratio DF : HJ = 12 : 9 = 12/9 = 4/3
This means that the side measures of ΔDEF are 4/3 times the corresponding side measures of ΔHGJ
Therefore, if HG = 6, then DE = 6 x 4/3 = 8
So: 2y + 4 = 8
⇒ 2y = 8 - 4 = 4
⇒ y = 4 ÷ 2 = 2
y = 2
Similarly, if GJ = 24, then EF = 24 x 4/3 = 32
So: 4x - 8 = 32
⇒ 4x = 32 + 8 = 40
⇒ x = 40 ÷ 4 = 10
x = 10
