Grades 7-8 Video Solutions 2021-video 2021 7-8/16

Video Transcription

Question 16. Five squares are positioned as shown. The smallest square indicated as an area of 1, as shown. What is the value of h? Take a closer look at our  diagram. We can start to notice some things. If we label the length of the second smallest square as x, then we know that the next square in size order has  a side length of x plus 1, since its side is equal to the smallest in the second smallest square, which we know has a side of 1 and the side we labeled as x. You  can write this down on the other sides of the squares. Now we notice another thing. The next square in size order will have a side length of x plus 1 plus 1,  since it is next to the one-sided square and the square with the side of x plus 1, so it has a side length of x plus 2. Now we notice that the largest square is  bordering the 1 square and the x plus 2 square, so when we add these together the side length is x plus 3, which can be written down here. Now we can notice  something interesting. The top side of our diagram has a length of x plus 1 plus x plus h, and the bottom side of our diagram has a length of x plus 2 plus x  plus 3, and these two are the same length. Knowing this, we can set both sides equal to each other. When we combine like terms, we get 2x plus 1 plus h equal to 2x  plus 5. We subtract out the x's on both sides, we're left with 1 plus h plus 5. All we have to do is to solve for h. With this simple formula, we know that our answer will be C, 4.

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