Johanna buys two poster frames that have the same area, but different shapes. One is a rectangular frame with a width of 40 inches and a length of 30 inches. The other frame is square. What a poster with dimensions of 36 inches X 36 inches fit in the square frame?

No, the poster would not fit in the frame

Step-by-step explanation:

A rectangle is a quadrilateral (has 4 sides and 4 angles) with two pair of opposite and equal sides.

A square is a quadrilateral in which all sides are equal.

Given that the rectangular frame has a width of 40 inches and a length of 30 inches. The area of the rectangular frame is:

Area of rectangular frame = length * breadth = 40 inches * 30 inches = 1200 in²

Since the square frame has the same area as the rectangular frame, hence:

Area of square frame = length * length

length² = 1200

length = √1200 = 34.64

Therefore the dimensions of the square frame is 34.64 inches by 34.64 inches.

Hence a poster with dimensions of 36 inches X 36 inches cannot fit in the square frame.