The isosceles triangles below are similar.
a. What is the similarity ratio of triangle EFG to triangle HIJ? Simplify your ratio.
b. What is the value of x?
c. What is the perimeter of each triangle? (Hint: use Pythagorean Theorem).
d. What is the ratio of the Perimeter of Δ EFG to Perimeter of Δ HIJ? Simplify your ratio.

a) 2:1. b) 3. c) Perimeter of ΔEFG=36 Perimeter of ΔHIJ=18. d) 2:1

Step-by-step explanation:

a) Find the ratio of GF and JI. 16:8. Simplify by dividing both by 8 to get 2:1.

b) Set up this equation: 6/16=x/8. Cross-multiply. 6*8=48. Divide by 16. 48/16=3.

c) First find the length of one half of GF by dividing 16 by 2. 16/2=8. Set up the Pythagorean theorem. 8^2+6^2=c^2. Square 8 and 6. 64+36=c^2. Add 64 and 36. 100=c^2. Find the square root of 100. c=10.

EF and EG both measure 10 since they are shown to be congruent. 10+10+16=36.

Next find the length of one half of JI by dividing 8 by 2. 8/2=4. Set up the Pythagorean theorem. Since we know x=3, it will be 4^2+3^2=c^2. Square both 4 and 3. 16+9=c^2. Add 16 and 9. 25=c^2. Find the square root of 25. c=5.

HJ and HI both measure 5 since they are congruent. 5+5+8=18.

d) Find the ratio of the perimeters of ΔEFG and ΔHIJ. 36:18. Simplify by dividing both by 6 to get 6:3. Simplify further by dividing both by 3 to get 2:1.

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step-by-step explanation:

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