Question

The rectangle is 2 cm wider and 5 cm longer than a square. The area of the rectangle is 38 cm greater than the square. What are the dimensions of the rectangle?

Answer 1

the rectangle has dimensions of 6cm x 9 cm

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