Question

17)
there are two rectangles. the first rectangle has a top side length of 9, left and right side lengths of 13, and the bottom side length is marked as x. the second rectangle has top and bottom side lengths of 90, and left and right side lengths of 130.

Explanation:

Step1: Identify the relationship

The two rectangles seem to be similar (same shape, different sizes). For similar rectangles, the ratios of corresponding sides are equal. So, $\frac{9}{90}=\frac{13}{130}=\frac{x}{?}$ Wait, actually, let's check the sides. The first rectangle has length 13 and width 9, the second has length 130 and width 90. Notice that 130 is 13×10 and 90 is 9×10. So the scale factor is 10. But wait, the first rectangle's bottom side is x, which should correspond to the second's bottom side (90). Wait, no, the first rectangle: top is 9, right is 13, bottom is x, left is 13. So it's a rectangle, so top and bottom should be equal, left and right equal. Wait, maybe I misread. Wait, the first rectangle: top 9, right 13, bottom x, left 13. So it's a rectangle, so top = bottom, left = right. Wait, but the second rectangle: top 90, right 130, bottom 90, left 130. So it's a rectangle too. Wait, maybe the problem is to find x? But in a rectangle, opposite sides are equal, so x should be equal to the top side, which is 9. Wait, that can't be. Wait, maybe the two rectangles are similar, so the ratio of length to width is the same. For the second rectangle, length is 130, width is 90? Wait, no, 130 and 90: 130/90 = 13/9. For the first rectangle, length 13, width 9. So 13/9 = 130/90, which is true (130÷10=13, 90÷10=9). So the first rectangle's bottom side x should be equal to the top side, which is 9. Wait, maybe the diagram has a typo, but assuming it's a rectangle, opposite sides are equal. So x = 9.
Wait, maybe I misinterpret. Let's re-examine. The first rectangle: top 9, right 13, bottom x, left 13. So it's a rectangle, so top and bottom are equal, so x = 9. The second rectangle: top 90, right 130, bottom 90, left 130. So it's a rectangle with length 130 and width 90, and the first is length 13 and width 9, so scale factor 10. So x, being the bottom side of the first rectangle, should equal the top side, which is 9.

Step2: Confirm with rectangle properties

In a rectangle, opposite sides are congruent (equal). So for the first rectangle, top side is 9, so bottom side (x) must also be 9.

Answer:

9