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Gala2k [10]
3 years ago
10

In Triangle BCD, BC=BD, and angle B =13x-35, angle C = 5x-19, angle D=2x+14. Find the measure of each angle

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
5 0

Answer:

B = 108

C = 36

D = 36

Step-by-step explanation:

Given

B =13x - 35

C = 5x - 19

D=2x+14

BC = BD

Required

Determine the measure of each angle

The angles in a triangle sum up t 180. i.e.

B + C + D = 180

Since BC = BD, then C = D

B + C + D = 180 can then be rewritten as:

B + C + C = 180

B + 2C = 180

Substitute values for B and C

13x - 35 + 2(5x - 19) = 180

Open Bracket

13x - 35 + 10x - 38 = 180

Collect Like Terms

13x + 10x = 180 + 38 + 35

23x= 253

Divide both sides by 23

x = 11

To get the measure of each angle, substitute 11 for x in the expressions of B, C and D

B =13x - 35

B = 13 * 11 - 35

B = 108

C = 5x - 19

C = 5 * 11 - 19

C = 36

D=2x+14

D = 2 * 11 + 14

D = 36

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NemiM [27]

Answer:

(1)Base Area= 81 square yards.

(2)

  • 3 ft long and 16 ft wide
  • 6 ft long and 8 ft wide
  • 24 ft long and 2 ft wide

(3)Height=12 Units

Step-by-step explanation:

<u>Question 1</u>

Volume of the rectangular prism=2,592 cubic yards.

Height of the rectangular prism=32 yards

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=2592

32lb=2592

lb=2592/32=81

Base Area= 81 square yards.

<u>Question 2</u>

Volume of the rectangular prism=432 cubic feet.

Height of the rectangular prism=9 feet

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=432

9lb=432

lb=432/9=48

Base Area= 48 square yards.

Any dimension whose product is 48 is a possible choice.

They are:

  • 3 ft long and 16 ft wide
  • 6 ft long and 8 ft wide
  • 24 ft long and 2 ft wide

<u>Question 3</u>

<u />

Volume of the rectangular prism=960 cubic units.

Base Area of the rectangular prism, lb=80 Square Units

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=960

80h=960

h=960/80=12

Height= 12 units.

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