# Video: Finding the Area of a Square given the Dimensions of a Rectangle Having the Same Area

If a square and a rectangle have equal area, and the rectangle measures 18 cm by 50 cm, what is the length of the square?

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### Video Transcript

If a square and rectangle have equal area, and the rectangle measures 18 centimeters by 50 centimeters, what is the length of the square?

We know that the dimensions of the rectangle are 18 centimeters and 50 centimeters. We will let the length of the square be 𝐿 centimeters. The area of any rectangle can be calculated by multiplying the length by the width. In this question, this is equal to 50 multiplied by 18. As five multiplied by 18 is 90, 50 multiplied by 18 is equal to 900. The area of the rectangle is equal to 900 square centimeters.

We can calculate the area of a square by squaring its length. In this question, this will be equal to 𝐿 squared, as 𝐿 multiplied by 𝐿 is 𝐿 squared. The area of the square and rectangle are equal, so 𝐿 squared is equal to 900. The inverse or opposite of squaring is square rooting, so we need to square root both sides of this equation. The square root of 900 is equal to 30, as 30 multiplied by 30 is 900. We can therefore conclude that the length of the square is 30 centimeters.