# Question Video: Finding the Length of a Rectangle Similar to Another Rectangle given the Dimensions of the Second Rectangle Mathematics • 8th Grade

Given that the rectangle π΄π΅πΆπ· is similar to the rectangle ππ΅ππ, find the length of line segment ππ.

02:41

### Video Transcript

Given that the rectangle π΄π΅πΆπ· is similar to the rectangle ππ΅ππ, find the length of line segment ππ.

We are told in the question that the rectangles π΄π΅πΆπ· and ππ΅ππ are similar. This means that theyβre enlargements or dilations of each other. The corresponding lengths in each rectangle will, therefore, be in the same ratio. The ratio of side lengths ππ and π΄π· will be equal to the ratio of side lengths ππ and πΆπ·. Substituting the lengths in centimeters from our diagram, we have ππ over 80 is equal to 21 over 84. The right-hand side simplifies to one-quarter by dividing the numerator and denominator by 21. We can then multiply both sides of this equation by 80. One-quarter multiplied by 80 is equal to 20. This means that the line segment ππ is equal to 20 centimeters.

We can now use the smaller rectangle to find the length of ππ. The Pythagorean theorem states that, in any right triangle, π squared plus π squared is equal to π squared, where π and π are the lengths of the shorter sides of the right triangle and π is the length of the hypotenuse. In the right triangle πππ, ππ is the hypotenuse. Therefore, ππ squared plus ππ squared is equal to ππ squared. Substituting in the lengths of ππ and ππ, the left-hand side becomes 20 squared plus 21 squared. 20 squared is equal to 400, and 21 squared is 441. These sum to give us 841. We can then take the square root of both sides of our equation. The square root of 841 is 29.

If the two rectangles π΄π΅πΆπ· and ππ΅ππ are similar, the length of the line segment ππ is 29 centimeters.