Question - Finding Side Lengths of Similar Polygons
Solution:
The image shows two similar polygons labeled GHJK and RQTS. To find the side lengths RS and TU, we'll use the properties of similar polygons. In similar polygons, the ratios of the corresponding side lengths are equal.From the image, we can see the corresponding side lengths of the polygons as follows:GH (45 units) corresponds to RQ (unknown)HJ (27 units) corresponds to QS (37 units)JK (18 units) corresponds to ST (unknown)KG (36 units) corresponds to TR (52 units)To find the length of RS, we compare the ratios of HJ to QS (which we know) with the ratio of GH to RQ (which we need to find out):HJ/QS = GH/RQ27/37 = 45/RQNow, let's solve for RQ (denoted as RS in the question):RQ = (45 * 37) / 27Calculate the value of RQ:RQ = 1665 / 27 ≈ 61.667So, RS ≈ 61.7 (rounded to one decimal place).To find the length of TU (which corresponds to JK in the larger polygon), we'll set up a similar ratio. This time, we'll use the sides KG and TR since their lengths are known:JK/ST = KG/TR18/TU = 36/52Now solve for TU:TU = (18 * 52) / 36Calculate the value of TU:TU = 936 / 36 = 26The length of TU is exactly 26 units.Therefore, RS ≈ 61.7 and TU = 26.
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