Dimensions of a Mat

Question

A square mat has a red border on all four sides, the rest of the mat is blue. The width of the blue square is three-fourths the width of the entire square. If the area colored red is 28m^2, determine the length of each side of the mat.

Answer 1

Draw a diagram

w is the width of the entire square (it is also the length!)

0.75w is the width of the blue insides

w² - (0.75w)² = 28

 

Can you solve for w?