+257 A quadrilateral has two pairs of congruent sides and a longer diagonal of length 6, as shown. For what value of x will the area of the shaded area be 40% of the area of the unshaded region?
+12530 A quadrilateral has two pairs of congruent sides and a longer diagonal of length 6, as shown. For what value of x will the area of the shaded area be 40% of the area of the unshaded region?
+129852 We only need to look at the top two triangles.....they are under the same height.....and the areas of triangles under the same height are to each other as their bases
So.......
x / (6 - x) = .40 cross-multiply
x = .40 (6 - x)
x = 2.4 - .4x
1.4x = 2.4
x = 2.4/1.4 = 12/7
Proof : [ 2* area of triangle on the left ] / [ 2 * area of triangle on the right ] =
[ 2 * triangle height * base length of left triangle ] / [ 2 * triangle height * base length of right triangle ] =
[ base length of triangle on the left ] / [ base length of triangle on the right ]
[12/ 7 ] / [ 6 - 12/7 ] =
[ 12/7 ] / [ 42/7 - 12/7 ] =
[12/7 ] / [ 30/7] =
[ 12/7] * [ 7/30 ] =
12/30 =
4/10 =
.40 = 40%
