Answer:
x = 7
Step-by-step explanation:
Similar figures have sides that are proportional. Setting up a proportion for the sides of the figures will help solve for 'x':
Cross-multiply: 3(x + 1) = 6(x - 3)
Distribute: 3x + 3 = 6x - 18
Combine like terms: 21 = 3x
Solve for 'x': x = 7
Area of the wall = 8 x 19 = 152 ft square
Area of the window = 4 x 5 = 20 ft square
Area of 3 windows = 20 x 3 = 60 ft square
The percent area of 3 windows from area of the wall = 60/152 or approximately .395 or 39.5%
Answer:
∠BIJ ≅ ∠CGJ and ∠BJI ≅ ∠CJG
Step-by-step explanation:
We have that the initial triangles are equal. Let us check which components remain within the final triangles as the same. The only such components are the angles B and C. We now know that we have to apply a triangle equality criterion.
The triangles BGH and CIH are equal since the have 2 common sides and the respective interior angles are equal. Then we have that BI=GC and also that the respective angles B and C are equal. THen also HIJ=HGJ since they fill to 180 degrees with angles that are equal.
Hence by angle-side-angle the triangles BJI and CJG are equal.
∠BIJ ≅ ∠CGJ and ∠BJI ≅ ∠CJG
