1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
elixir [45]
3 years ago
13

The longer leg of a right triangle is 6cm longer than the shorter leg and also 1cm longer than the hyptenese. find the perimeter

of the triangle.
Mathematics
1 answer:
CaHeK987 [17]3 years ago
5 0
X - a leg  (x > 6);
x - 6 - a leg;
x + 1 - a <span>hypotenuse;</span>
Use the Pythagorean theorem
(x+1)^2=x^2+(x-6)^2

Use:(a\pm b)^2=a^2\pm2ab+b^2

x^2+2x+1=x^2+x^2-12x+36\ \ \ |-x^2-2x-1\\\\x^2-14x+35=0\ \ \ |-35\\\\x^2-14x=-35\\\\x^2-2\cdot x\cdot7=-35\ \ \ |+7^2\\\\x^2-2\cdot x\cdot7+7^2=-35+7^2\\\\(x-7)^2=14\iff x-7=\pm\sqrt{14}\ \ \ |+7\\\\x=7-\sqrt{14} < 6;\ x=7+\sqrt{14}

x=7+\sqrt{14}\\x-6=1+\sqrt{14}\\x+1=8+\sqrt{14}

The perimeter:

7+\sqrt{14}+1+\sqrt{14}+8+\sqrt{14}=16+3\sqrt{14}
You might be interested in
Jordan is picking berries. The number of blueberries he
inna [77]
D. x/3 - 5
--------------
4 0
3 years ago
-4z ≥ - 64.4
nignag [31]

Answer: D

Step-by-step explanation:

5 0
2 years ago
Mr. Smith decided to regularly wash his head with an antidandruff shampoo every three days. He began on January 1st, 2017 on Sat
mezya [45]

Answer:

If the first day is January 1st, 2017 on a "sunday"(Not saturday), that means that the last day is December 31, 2017 on a sunday. (Pog moment for mee)

Step-by-step explanation:

3 0
3 years ago
What is the completely factored form of this polynomial?<br> – 8x²+<br> + 16
Zanzabum

Answer:

-8(x²-2)

Step-by-step explanation:

Factor -8 out of -8x²

-8(x²)+16

Factor -8 out of 16.

-8(x²)-8(-2)

Factor -8 out of -8(x²)-8(-2).

7 0
2 years ago
you make homemade lip balm about 11% of the lip balm is made from beeswax you make 4 2/5 teaspoons of of the lip balm about how
o-na [289]
≈ 1/2 teaspoon
4 2/5 * .11 = .484 teaspoon
7 0
3 years ago
Other questions:
  • What is the solution to this inequality: -4(3x-5)&lt;2(3x+4)​
    13·1 answer
  • Today, Nate has 100 bananas. He will eat 2 of them every day.
    7·2 answers
  • Noah built a fenced dog run that is 8 yards long and 6 yards wide. he placed posts at every corner and every yard along the leng
    6·2 answers
  • Zack is taking inventory of loaves of bread at the grocery store where he works. There are 20 loaves in a full case, and Zack ha
    13·1 answer
  • Will give brainliest! please answer correctly!
    6·1 answer
  • 7.5 as an improper fraction in its simplest form
    14·1 answer
  • What is the quotient 2 1/5 over negative 1/10​
    13·2 answers
  • Find the equation of the linear function represented by the table below in slope-intercept form
    7·1 answer
  • 30 18 24 4 = 18 make it true
    6·2 answers
  • The temperature of the pool water started at 82 degrees, and it is cooling down 0.4 degrees each hour. If the water temperature
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!