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∆ABC is an isosceles triangle. The length of CB is 12 feet 4 inches and the congruent sides are

each 3/4 this length.

2. What is the perimeter of ∆ABC?

a. 31 ft. 4 in.

b. 21 ft. 7 in.

c. 30 ft. 10 in.

d. 18 ft. 6 in.

3. In ∆DEF, DE and DF are each 6 feet 3 inches long. This length is 0.75 times the length of

FE. What is the perimeter of ∆DEF?

a. 12 ft. 4 in.

b. 17 ft. 2 in.

c. 14 ft. 7 in.

d. 20 ft. 10 in.

4. ∆JKL is an isosceles triangle with JL ≅ KL. If JK is three more than x, KL is 17 less than four

times x, and JL is 45 less than six times x, find x and the measure of each side.

e. 39, 39, 17

f. 17, 15, 17

g. 17,17,39

h. 42,42,42​

User Jimzie
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1 Answer

4 votes

Answer:

Answer for 2nd is option c, for 3rd is option d, for 4th is option e

Explanation:

As we know 1 ft.=12 in.

  1. In ΔABC

∴ The congruent sides are AB and AC respectively

  • CB =12 ft. 4 in.=148 in.
  • AB=
    (3)/(4)CB =111 in. =9 ft. 3 in.
  • AC=
    (3)/(4)CB =111 in. =9 ft. 3 in.

Perimeter of ΔABC =AB+AC+CB

=9 ft. 3 in. + 9 ft. 3 in. +12 ft. 4 in.

=30 ft. 10 in.

2. In ΔDEF

∴ The congruent sides are DE and DF respectively

  • DE = 6 ft. 3 in. =75 in.
  • DF = 6 ft. 3 in. =75 in.
  • Let the length of FE is equal to x
  • 0.75FE =DE =DF
  • 0.75x = 6 ft. 3 in. =75 in.
  • x =100 in. =8 ft. 4 in.

Perimeter of ΔDEF =DE+DF+FE

= 6 ft. 3 in. +6 ft. 3 in. +8 ft. 4 in.

= 20 ft. 10 in.

3. In ΔJKL

∴ The congruent sides are JL and KL respectively

  • JK = x+3
  • KL =4x-17
  • JL =6x-45
  • JL≅KL
  • 4x-17 =6x-45 . . . . . . . . . . . . . . . . . . . . . . . (1)
  • Subracting 4x from both sides from eq 1
  • -17 =2x-45
  • Adding 45 on both the sides
  • 28 =2x
  • Dividing by 2 on both sides
  • 14 =x
  • JK = 14+3 =17
  • KL = 4×14-17 =39
  • JL = 6×14-45 =39

The dimensions of the ΔJKL are 39,39 and 17.

User UneXp
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6.3k points