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3 years ago

In triangle ABC, angle A is equal to angle C, BA=x+20,CA=4x-30, and BC=3x+14. What is the length of BC?

Mathematics

1 answer:

Anna [14]3 years ago

3 0

Answer:

BC = 23

Step-by-step explanation:

Since ∠ A = ∠ C then the triangle is isosceles with AB = BC, that is

3x + 14 = x + 20 ( subtract x from both sides )

2x + 14 = 20 ( subtract 14 from both sides )

2x = 6 ( divide both sides by 2 )

x = 3

Thus

BC = 3x + 14 = 3(3) + 14 = 9 + 14 = 23

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Step-by-step explanation:

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3 years ago

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3 years ago

triangle ABC is isosceles, angle B is vertex angle , AB = 20x -2, AC =25x, and BC =12 x +20. Find x and the length of each side

lisov135 [29]

Length of AB = 18. 92

Length of AC = 26. 15

Length of BC = 32. 552

<h3>How to determine the sides of the triangle</h3>

Using the Pythagorean theorem, we have that

$(20 x-2)^2 = (12x + 20)^2 + (25x)^2$

Expand the bracket

$400x^2- 4 = 144x^2 + 400 + 625x^2$

Collect like terms

$400x^2 - 144x^2 - 625x^2 = 400 + 4$

$-369x^2 = 404$

Make x^2 subject

$x^2 = \frac{404}{369}$

$x = \sqrt{1.0948}$

$x = 1. 046$

Thus,

Length of AB = 20x -2 = 20(1. 046) - 2 = 18. 92

Length of AC = 25x = 25* 1.046 = 26. 15

Length of BC = 12x + 20 = 12(1. 046) + 20 = 32. 552

Learn more about isosceles triangles here:

brainly.com/question/1475130

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8 0

1 year ago

a store sign reads "Take 75% of the original price when you take an additional 15% off the sale price, which is 60% off the orig

ExtremeBDS [4]

Answer:

The new price is 66% off the original not 75% off

Step-by-step explanation:

Let x be the original price

First take 60 percent off

x - x*60% = new price

x- .60x = .40x

The new price is .40x

Then take 15 % off

(.40x) - (.40x)*15%

.40x - .40x*.15

.40x - .06x

.34x

100 -.34 =.66

The new price is 66% off the original not 75% off

3 0

3 years ago

In triangle ABC, angle A is equal to angle C, BA=x+20,CA=4x-30, and BC=3x+14. What is the length of BC?​

In triangle ABC, angle A is equal to angle C, BA=x+20,CA=4x-30, and BC=3x+14. What is the length of BC?