Question

∆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​

Answer 1

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.