Question

The diagonals of a trapezoid are perpendicular and have lengths 8 and 10. find the length of the median of the trapezoid.

Answer 1

We have to use Pythagorean theorem ( see the picture in the attachment ):
( a + b )² = 10² + 8²  ( where a and b are the bases of a trapezoid )
( a + b )² = 100 + 64
( a + b )² = 164
a + b = √164
a + b = 12.8 
We don`t need to find a and b, because we have a formula for the length of the median which is:
m = ( a + b ) / 2 
m = 12.8 / 2
Answer:
m = 6.4

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Answer 2

The length of the median of the trapezoid is $\boxed{12.80}.$

Further explanation:

The median is a line that divides the trapezoid into two equal halves that has same area.

The formula to calculate the median of the trapezoid can be expressed as follows,

$\boxed{{\text{Median}}=\sqrt {A{C^2} + B{D^2}}}$

Here, AC and BD are the diagonals of the trapezoid.

Given:

The diagonals of a trapezoid are perpendicular to each other and have lengths 8 and 10.

Explanation:

The lengths of the diagonals are 8 and 10.

The length of the median of the trapezoid can be calculated as follows,

$\begin{aligned}{\text{Median}}&= \sqrt {A{C^2} + B{D^2}}\\&=\sqrt {{8^2} + {{10}^2}}\\ &= \sqrt {64 + 100}\\&= \sqrt {164}\\&= 12.80\\\end{aligned}$

The length of the median of the trapezoid is $\boxed{12.80}.$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Trapezoid

Keywords: triangle, triangle pair, equal angles, sides, area, trapezoid, two triangles, bases, intersecting, diagonal, segment, sector, minor segment, median, perpendicular, lengths, 8, 10, length of the median.