Answer:
the rectangle has dimensions of 6cm x 9 cm
Step-by-step explanation:
denoting as 'a' the shorter side of the rectangle , 'b' as the longer side of the rectangle and 'L' as the side length of the square, then
a=L+2
b=L+5
the area Aof the rectangle is
A=a*b
since the area is of the square is L² , then
A=38+L²
replacing the values
A=(L+2)*(L+5) = L² + 5*L+2*L+10 = L² + 7*L + 10
38+L² = L² + 7*L + 10
38 = 7*L + 10
7*L= 28
L= 28/7 = 4 cm
then from the first equations
a=L+2 cm = 4 cm + 2 cm = 6 cm
b= L + 5 cm = 4 cm + 5 cm = 9 cm
therefore the rectangle has dimensions of 6cm x 9 cm
