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Rainbow [258]
3 years ago
6

ABC is not an acute triangle what is the first step of indirectly proving this statement

Mathematics
1 answer:
dmitriy555 [2]3 years ago
5 0

Answer:

Assume ΔABC is an acute triangle.

Step-by-step explanation:

Given the triangle ABC.

We have to tell the first step of indirect proving ΔABC is not an acute triangle.

An indirect proof, also known a proof by contradiction. When we use indirect proof method, we assume the opposite of our theory to be true and then by applying our assumed theory we contradict the given statement which proves our supposition is wrong. In other words, we assume our theory is false.

Hence, our first step is to

Assume ΔABC is an acute triangle.

Third option is correct.

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Jack has a rectangular patio with a length that is one foot less than twice its width. His neighbor Ron's patio has the same wid
swat32

Answer:

difference in area = 16 ft²

if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft

if you use 13 the difference i length will be 25 - 18 = 7 ft

Step-by-step explanation:

Jacks rectangular patio

width = a

length = 2a - 1

area = lw

where

l = length

w = width

area = 120 ft²

a(2a - 1)

2a² - a - 120 = 0

(a - 8) (2a + 15)

a = 8 or -15/2

Ron's rectangular patio

width = a

length = a + 5

area = lw

area = 104 ft²

a (a + 5) = 104

a² + 5a -104 = 0

(a + 8)  (a - 13)

a = -8 or 13

How many square feet longer is jack patio longer than Ron's patio is the difference in their area. Therefore,

120 - 104 = 16 ft²

The value 8 or 13 can be used for a since the width a have to be the same.

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if you use 13 the difference i length will be 25 - 18 = 7 ft

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