Question

quadrilateral bcde is similar to quadrilateral fghi. find the measure of side hi. round your answer to the nearest tenth if necessary. figures are not drawn to scale. answer attempt 1 out of 2

Explanation:

Step1: Identify corresponding sides

Since quadrilateral BCDE ~ quadrilateral FGHI, the ratio of corresponding sides is equal. Side ED (26) corresponds to side IF (56)? Wait, no, wait. Wait, side EB is 17, and side HI corresponds to EB? Wait, let's check the order. BCDE and FGHI: so B corresponds to F? Wait, no, the order of the letters: BCDE ~ FGHI, so B->F, C->G, D->H, E->I? Wait, no, maybe E->I, D->H, C->G, B->F? Wait, looking at the figures: BCDE has E to D as 26, E to B as 17. FGHI has I to F as 56, H to I as the side we need. Wait, maybe ED corresponds to IF? No, ED is 26, IF is 56? Wait, no, maybe EB corresponds to HI, and ED corresponds to IF? Wait, let's get the correspondence right. In similar figures, the order of the vertices matters. So BCDE ~ FGHI means B corresponds to F, C to G, D to H, E to I. So side EB (from E to B) in BCDE corresponds to side HI (from H to I) in FGHI? Wait, no, E to B is 17, H to I is the side we need. And side ED (E to D) is 26, and side IF (I to F) is 56? Wait, no, I to F is 56, E to D is 26. Wait, maybe the ratio of similarity is (IF)/(ED) = 56/26, and then HI corresponds to EB. So EB is 17, so HI = EB * (IF/ED). Let's check:

So corresponding sides: EB (17) in BCDE corresponds to HI in FGHI. ED (26) in BCDE corresponds to IF (56) in FGHI. So the ratio of similarity is IF/ED = 56/26. Therefore, HI = EB (IF/ED) = 17 (56/26).

Step2: Calculate the ratio

First, simplify 56/26: divide numerator and denominator by 2: 28/13 ≈ 2.1538.

Step3: Multiply by 17

17 (28/13) = (1728)/13 = 476/13 ≈ 36.615... Rounded to the nearest tenth is 36.6? Wait, no, wait: 476 divided by 13: 13*36 = 468, 476-468=8, so 36 + 8/13 ≈ 36.615, which is 36.6 when rounded to the nearest tenth? Wait, no, 8/13 is approximately 0.615, so 36.615 is 36.6 when rounded to the nearest tenth? Wait, no, 0.615 is closer to 0.6 or 0.7? 0.615 is 0.6 when rounded to the nearest tenth (since the hundredth digit is 1, which is less than 5? Wait, no: 36.615, the tenths place is 6, hundredths is 1, so we round down, so 36.6? Wait, no, 36.615: the tenths digit is 6, hundredths is 1, so yes, 36.6 when rounded to the nearest tenth. Wait, but let's check the calculation again.

Wait, maybe the correspondence is different. Let's re-examine the figures. BCDE: E---D (26), E---B (17). FGHI: I---F (56), H---I (the side we need). So maybe E---D corresponds to I---F? So ED = 26, IF = 56. Then EB = 17 corresponds to HI. So the ratio of similarity is IF/ED = 56/26. Then HI = EB (IF/ED) = 17 (56/26). Let's compute that:

56 divided by 26 is approximately 2.1538. Multiply by 17: 17 * 2.1538 ≈ 36.615, which is approximately 36.6 when rounded to the nearest tenth.

Answer:

36.6