Answer:
w = 11 , x = 25
Explanation:
for Δ ABC ≅ Δ TUV, then corresponding sides must be congruent, that is
AB = TU and BC = UV ( using these to create 2 equations )
- 9x + 20w + 89 = 4w + x + 15 ( subtract 4w + x + 15 from both sides )
- 10x + 16w + 74 = 0 → (1)
and
x + w + 41 = - 18w + 11x ( subtract - 18w + 11x from both sides )
- 10x + 19w + 41 = 0 → (2)
multiplying (2) by - 1 and adding to (1) will eliminate x
10x - 19w - 41 = 0 → (3)
add (1) and (3) term by term to eliminate x
0 - 3w + 33 = 0 ( subtract 33 from both sides )
- 3w = - 33 ( divide both sides by - 3 )
w = 11
substitute w = 11 into either of the 2 equations and solve for x
substituting into (1)
- 10x + 16(11) + 74 = 0
- 10x + 176 + 74 = 0
- 10x + 250 = 0 ( subtract 250 from both sides )
- 10x = - 250 ( divide both sides by - 10 )
x = 25
thus the values x = 25 and w = 11 will make the triangles congruent