Exactly Three-quarters

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

The area of the rectangle is $48cm^2$, so the unshaded area is $12cm^2$. Therefore taking the two unshaded triangles together: ($1/2\times x\times2$) + ($1/2\times(6-x)\times8$) $= 12$ which means that $x + 24 - 4x = 12$, so $x = 4$.

This problem is taken from the UKMT Mathematical Challenges.
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