In the figure, not drawn to scale, 40% of the triangle UXW is shaded. The ratio of the shaded part of the circle to the unshaded part of the circle is 5 : 9. What percentage of the rectangle TUWV is unshaded?
Shaded Circle |
Unshaded Circle |
Shaded Triangle |
Total Triangle |
5x2 |
9x2 |
2x5 |
5x5 |
10 u |
18 u |
10 u |
25 u |
40% =
40100 =
25 The shaded part of the figure is the repeated identity. Make the shaded part of the figure the same. LCM of 2 and 5 is 10.
Total area of the rectangle
= 2 x Total triangle
= 2 x 25 u
= 50 u
Unshaded areas
= 50 u - 10 u
= 40 u
Percentage of Rectangle TUWV that is unshaded
=
Unshaded areasArea of Rectangle TUWV x 100%
=
4050 x 100%
= 80%
Answer(s): 80%