Answer:
x = 12°
y = 1.4 cm
Step-by-step explanation:
1. Because the two triangles are similar, their corresponding angles are congruent.
so
3x + 14 = 50
Subtract 14 from both sides
3x = 36
Divide both sides by 3
x = 12
x = 12° (remember units)
Check work:
3(12) + 14 = 50
36 + 14 = 50
50 = 50
2. Because the two triangles are similar, their corresponding sides are in equal proportion.
Two sides of triangle ABE are
5.6 and 4
And two corresponding sides of triangle ACD are
5.6 + y and 5
So
5.6 / 4 = (5.6 + y) / 5
Cross multiply
5.6 * 5 = 4(5.6 + y)
Multiply 5.6 * 5 on the left
28 = 4(5.6 + y)
Distribute the 4 to each term
28 = 4*5.6 + 4*y
Simplify the right side
28 = 22.4 + 4y
Subtract 22.4 from both sides
5.6 = 4y
Divide by 4 on both sides
1.4 = y
y = 1.4 cm (remember units)
Check our work:
5.6/4 = (5.6 + 1.4)/5
1.4 = 7/5
1.4 = 1.4
