Answer:
x=12
Step-by-step explanation:
The isosceles triangle is made up of 222 congruent right triangles.
The base of each right triangle is \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction the base of the isosceles triangle.
Hint #22 / 6
When we have a right triangle we can use the Pythagorean Theorem to solve for a missing side.
The equation for the Pythagorean Theorem is
a^2 + b^2 = c^2a
2
+b
2
=c
2
a, squared, plus, b, squared, equals, c, squared
where aaa and bbb are the lengths of the two legs of the triangle, and ccc is the length of the hypotenuse.
[How can I tell which side is the hypotenuse?]
Hint #33 / 6
First we can find the missing length for one of the right triangles. Let's label the drawing with aaa, bbb, and ccc:
Note that aaa and bbb could be switched because they are legs.
Hint #44 / 6
Let's use the Pythagorean Theorem to solve for xxx.
\begin{aligned} \blueD a^2 + \greenD b^2 &= \goldD c^2 ~~~~~~~~~\small\gray{\text{The Pythagorean Theorem}}\\\\ \blueD{a}^2 + \greenD{ 8}^2 &= \goldD{10}^2 ~~~~~~~\small\gray{\text{Plug in the side lengths}}\\\\ a^2 +64 &= 100 ~~~~~~\small\gray{\text{Evaluate } 8^2 \text{ and } 10^2}\\\\ a^2 &= 36~~~~~~~~\small\gray{\text{Subtract 64 from each side}}\\\\ a &= 6 ~~~~~~~~~~\small\gray{\text{Take the square root of each side}}\\\\ \\\end{aligned}
a
2
+b
2
a
2
+8
2
a
2
+64
a
2
a
=c
2
The Pythagorean Theorem
=10
2
Plug in the side lengths
=100 Evaluate 8
2
and 10
2
=36 Subtract 64 from each side
=6 Take the square root of each side
Hint #55 / 6
Since a=6a=6a, equals, 6 and aaa is half the length of xxx, we can multiply to find xxx.
x x x=a⋅2=6⋅2=12
Hint #66 / 6
x = 12x=12
