Answer:
The scale factor is 1/5
Step-by-step explanation:
Each of the lengths of the lengths of this triangle are divided by 5 (or multiplied by 1/5)
The numbers are "x" and "y", therefore, we suggest this system of equations:
x-y=14
xy=1800
We can solve by substitution method.
x=14+y
(14+y)y=1800
14y+y²=1800
y²+14y-1800=0
Now, we solve this square equation:
y=[-14⁺₋√(196+7200)] / 2=(-14⁺₋86)/2
We have two solutions:
y₁=(-14-86)/2=-50 ⇒x=14+y=14-50=-36
y₂=(-14+86)/2=36 ⇒x=14+y=14+36=50
Answer: we have two solutions:
Solution1: The first number is -36 and the other number is -50
Soltuion2: The first number is 50 and the other number is 36
Step-by-step explanation:
We know that the Pythagorean theorem is represented in the formula:
a^2 + B^2 = c^2
Where a and b are the legs of a right triangle, and c is the hypotenuse. Therefore, looking at the Pythagorean triples, we can infer that they are considered Pythagorean triples because they follow the Pythagorean theorem. To check if this is true, we can insert the numbers into theorem:
a^2 + b^2 = c^2
6^2 + 8^2 = 10^2
36 + 64 = 100
Since this equation is true, these three numbers could be the lengths of a right triangle, and are also therefore, a Pythagorean triple. We can also check the other three numbers:
a^2 + b^2 = c^2
5^2 + 12^2 = 13^2
25 + 144 = 169
Since this equation is also true, these three numbers could also be the side lengths of a right triangle, and are also therefore, a Pythagorean triple.
X+4+2x-10=2x+1
3x-6=2x+1
X-6=1
X=7
