Video Transcript
Given that 𝐴𝐵𝐶𝐷 is similar to 𝐸𝐹𝐺𝐻, determine the length of the line segment 𝐺𝐻.
It is important here to recognize what the approximation symbol denotes. It means that the two parallelograms drawn are similar. Two shapes are said to be similar if one is an enlargement or dilation of the other. This means that to calculate the length of one shape from the other, we can multiply by a scale factor and also that the corresponding lengths are in the same ratio. In this question, the ratio of the lengths 𝐺𝐻 to 𝐶𝐷 will be equal to the ratio of 𝐹𝐺 to 𝐵𝐶.
We are told in the diagram that 𝐶𝐷 is of length 35 inches, 𝐵𝐶 is of length 32 inches, and 𝐹𝐺 has length 96 inches. Substituting these values without units into the equation gives us 𝐺𝐻 over 35 is equal to 96 over 32. 96 and 32 are both divisible by 32. Therefore, the right-hand side simplifies to three over one. We can then multiply both sides of our equation by 35 such that 𝐺𝐻 is equal to three multiplied by 35. This is equal to 105. The line segment 𝐺𝐻 is therefore equal to 105 inches.
An alternative method here would be to notice that 96 is 32 multiplied by three. This means that the scale factor is equal to three. The parallelogram 𝐸𝐹𝐺𝐻 has dimensions three times as long as the parallelogram 𝐴𝐵𝐶𝐷. We can therefore multiply 35 inches, the length of 𝐶𝐷, by this scale factor of three to calculate the length of 𝐺𝐻. This, once again, gives us our answer of 105 inches.
