UKMT Grey Kangaroo, 2023

The diagram shows a smaller rectangle made from three squares, each of area $25\text{ cm}^2$, inside a larger rectangle. Two of the vertices of the smaller rectangle lie on the mid-points of the shorter sides of the larger rectangle. The other two vertices of the smaller rectangle lie on the other two sides of the larger rectangle. What is the area, in $\text{cm}^2$, of the larger rectangle?

(A) $125$ (B) $136$ (C) $149$ (D) $150$ (E) $172$