Geometry Strategy guide fourth edition P. 19 #10

[sanyu4]

I do not understand why they used the ending equasion: 21=10.5x? 10.5x represents the area for both the triangle and the ABCE, and 21 = only represents ABCE so how can 21=10.5x?

Thank you

[jnelson0612]

I do not understand why they used the ending equasion: 21=10.5x? 10.5x represents the area for both the triangle and the ABCE, and 21 = only represents ABCE so how can 21=10.5x?

Thank you

Look again! 10.5x represents the area of ABCE; we break ABCE into a small triangle with height 3 and base x, and a rectangle with height 3 and base 3x. Thus, the triangle would have area of (3*x)/2 or 1.5x, and the rectangle would have an area of 3*3x or 9x. 1.5x + 9x = 10.5x, and we know the area of ABCE is actually 21, thus x=2.