Find the value of xxx in the isosceles triangle shown below. Choose 1

x=12

Step-by-step explanation:

The isosceles triangle consist of two right angle triangle of the same dimensions.

Let the unknown side of the right angle triangle=y

x=y+y

x=2y

Right angle triangle

c^2=a^2+b^2

c=10

a=8

b=y

c^2-a^2=b^2

10^2-8^2=y^2

100-64=y^2

36=y^2

y=√36

=6

y=6

Recall

x=2y

Substitute the value of y into the equation

x=2(6)

=12

Therefore,

x=12

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