Exactly three-quarters
Weekly Problem 30 - 2007
Three-quarters of the area of the rectangle has been shaded. What is the length of x?
Three-quarters of the area of the rectangle has been shaded. What is the length of x?
Age
11 to 14
Challenge level
Problem
Image
Three-quarters of the area of the rectangle has been shaded.
What is the length of $x$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
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 $x = 4$.