Question

The isosceles triangles below are similar.

Answer 1

Answer: 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.