Which one of the following answers gives the value of (m+n)³ in terms of m³?

Question

In the figure, E, F, G and H are the midpoints of the sides of square ABCD.

The area of ABCD is m² and the area of DHIE is n²

Which one of the following answers gives the value of (m+n)³ in terms of m³?

a) 9/8 m³   b) 3m³  c) 27/8m³   d) 27m³  e) 125/64 m³

Answer 1

n² = 1/4m²  => n = 1/2m

(m+n)³ = (m + 1/2m)³ = (3/2m)³ = 27/8m³