As shown in the figure, draw three semicircles with the three sides of the right triangle as the diameter. If the areas of the two small semicircles are known to be S1 = 8 and S2 = 18, then S3 =? A.10 B.13 C.26 D.25

C
S1=(1/4)*PI*a^2
S2=(1/4)*PI*b^2
S3=(1/4)*PI*c^2=S1=(1/4)*PI*(a^2+b^2)=S1+S2=26

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1. As shown in the figure, it is known that in △ ABC, ∠ ACB = 90 °, take each side of △ ABC as an edge and make three squares outside △ ABC. S1, S2 and S3 represent the area of the three squares respectively. S1 = 81 and S2 = 225, then S3 = () A. 16B. 306C. 144D. 12
2. As shown in the figure, △ ABC is a right triangle, S1, S2 and S3 are squares, a, B and C are known to be the side lengths of S1, S2 and S3 respectively, then () A. b=a+cB. b2=acC. a2=b2+c2D. a=b+2c
3. As shown in the figure, take the three sides of RT △ ABC as the sides and make three equilateral triangles outwards. Their areas are represented by S1, S2 and S3 respectively. Please guess the quantitative relationship between S1, S2 and S3 and explain the reason
4. In Fig. 1, three semicircles are made outward with three sides of RT △ ABC as diameters, and their areas are expressed by S1, S2 and S3 respectively. It is not difficult to prove that S1 = S2 + S3. (1) (1) As shown in Figure 2, take the three sides of RT △ ABC as the sides and make three squares outward, and their areas are represented by S1, S2 and S3 respectively. Write down their relationship. (it is not necessary to prove) (2) As shown in Figure 3, take the three sides of RT △ ABC as the edges and make regular triangles outward, and their areas are represented by S1, S2 and S3 respectively. Determine their relationship and prove it; (3) If three general triangles are made outward with three sides of RT △ ABC, and their areas are expressed by S1, S2 and S3 respectively, what conditions should be satisfied for the triangle to have the same relationship with (2) between S1, S2 and S3?
5. Take the three sides of RT triangle ABC as the diameter and make three semicircles outwards. What is the quantitative relationship between their areas S1, S2 and S3?
6. Take the three sides of RT △ ABC as the edge, make three general triangles outward, and their areas are expressed by S1, S2, S3 respectively, to determine the relationship between S1, S2, S3
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8. The displacement of an object is S1 in the first 3 seconds and S2 in the last 3 seconds The displacement of an object in the first 3 seconds is S1, and that in the last 3 seconds is S2. Given s2-s1 = 6m, S1: S2 = 3:7, the total length of the inclined plane can be calculated The slide is accelerating. Let the length of slope be l and the total time be t L=a*t^2 / 2 S1=a *3^2 / 2 S2=L－[ a*( t －3)^2 / 2 ]=3at－4.5a 3/7=(a *3^2 / 2)/(3at－4.5a) T = 5 seconds 6=(3at－4.5a)－(a *3^2 / 2) a=1m/s^2 L = 12.5A = 12.5m
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