Answer:
The length of the rectangle is 6.
Step-by-step explanation:
Given: The diagonal of a rectangle is 10 and the height is 8.
Please understand, that a diagonal, divides the rectangle into two tringles.
To find the length of the rectangle, you can use Pythagoras on one of the right sided triangles, because the length of the triangle, is also the length of the rectangle!
<em>EXTRA:</em>
<em>If</em><em> you know the special 3 4 5 triangle, a so called Pythagorean Triple, then you can "see" the simularity between the numbers.</em>
<em>Instead of 5, a diagonal of 10 is given (factor of 2 bigger).</em>
<em>Instead of 4, the height of 8 is given (factor of 2 bigger</em><em>)</em><em>.</em><em> </em><em>By scaling the Pythagorean Triple 3 4 5 by a factor of 2, you get the numbers 6 8 10. Could it be, that the number we need to find, is six?</em>
Try to verify, by calculating the missing number (which is the length of the rectangle we are looking for).
a² + b² = c²
a = length (and is unknown)
b = height = 8
c = hypothenusa/diagonal = 10
Substitute the numbers given:
a² + 8² = 10²
Subtract 8² left and right of the = sign.
a² +8² -8² = 10² - 8²
a² + 0 = 100 - 64
a² = 36
a = + - √36
a = + - 6
<em>EXTRA</em><em>:</em>
<em>You</em><em> can ignore the -√36 = -6 part of the solution, because a length of -6 has no meaning here.</em>
a = 6
So, the length of the triangle is 6 and thus, the length of the rectangle is also 6.
.
and put the 
symbol in front of it. Don't multiply. This expresses the exact circumference.