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?

SydSu22 May 1, 2019

#1**0 **

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?

Omi67 May 2, 2019

#2**+2 **

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%

CPhill May 2, 2019