Question

Two squares are shown in the diagram . The larger square has sides of length 5x units. The smaller square has an area equal to ⅑ of the larger square . Find the length of the sides or the smaller square. Give your answer in the form a/b where a,b ∊ ℕ

Answer 1

From the information given,

length of side of the larger square = 5x units

The area of a square is calculated by the faormula,

area = length of side^2

Thus,

Area of larger square = (5x)^2 = 25x^2

The smaller square has an area equal to ⅑ of the larger square. This means that the area of the smaller square is

Area of smaller square = 1/9 * 25x^2 = 25x^2/9

Length of the side of square = square root of area

Thus,

Length of the sides of the smaller square = square root of (25x^2/9)

Length of the sides of the smaller square = 5x/3