Home -> Solved problems -> Find the length of the black segment

### Solution

To start, let’s simplify the geometric shape following the next steps.
Step 1:
Step 2: Let $$y$$ be the length of the purple segment
Now, we have a simplified version of the geometric shape. Let’s pick the right triangle in the next figure and apply Pythagoras theorem
$y^{2}=4^{2}+\left(3+5\right)^{2}$
$y^{2}=80$
Same thing for the upper right triangle
$y^{2}=x^{2}+3^{2}$
$\Rightarrow x^{2}+3^{2}=80$
$x^{2}=71$
$x>0$
$\huge \Rightarrow x=\sqrt{71}$
Home -> Solved problems -> Find the length of the black segment

### Related Topics: Solved Problems

How far apart are the poles ?
Determine the square's side $$x$$
How Tall Is The Table ?
Find the volume of the interior of the kiln
Error to avoid that leads to:
Why 0.9999999...=1
What's the problem ?
What values of $$x$$ satisfy this inequality
Prove that the function $$f(x)=\frac{x^{3}+2 x^{2}+3 x+4}{x}$$ has a curvilinear asymptote $$y=x^{2}+2 x+3$$
Why does the number $$98$$ disappear when writing the decimal expansion of $$\frac{1}{9801}$$ ?
Only one in 1000 can solve this math problem
Calculate the following
Find the limit of width and height ratio
Is $$\pi$$ an irrational number ?
Solve for $$x \in \mathbb{R}$$
Prove that $$e$$ is an irrational number
Prove that
Challenging problem
Solve the equation for $$x \in \mathbb{R}$$
Calculate the following limit
Calculate the following limit
Determine the angle $$x$$
Find the derivative of $$y$$ with respect to $$x$$
Solve the equation for real values of $$x$$
Find the equation of the curve formed by a cable suspended between two points at the same height
Calculate the sum of areas of the three squares
Calculate the integral
Prove Wallis Product Using Integration
Calculate the volume of Torus using cylindrical shells
Find the derivative of exponential $$x$$ from first principles
Find the volume of the square pyramid as a function of $$a$$ and $$H$$ by slicing method.
Prove that $\lim_{x \rightarrow 0}\frac{\sin x}{x}=1$
Prove that
Calculate the half derivative of $$x$$
Find out what is a discriminant of a quadratic equation.
Calculate the rectangle's area
Determine the square's side $$x$$
Wonderful math fact: 12542 x 11 = 137962
Calculate the sum
What is the new distance between the two circles ?
Solve the equation for $$x\epsilon\mathbb{R}$$
Calculate the area of the Squid Game diagram blue part
Calculate the limit
Find the infinite sum
Calculate the integral
Prove that
Can we set up this tent ?
Find the value of $$h$$
Is the walk possible?
Find the length of the black segment
Home -> Solved problems -> Find the length of the black segment