Question

In trapezoid ABCD, AB || CD, MZA=90°, AD=8 in, DC=9 in, CB=10 in, and ZB is
acute. Find DB.

Answer 1

`\[DB = √(145)`, { which simplifies to } DB =
`7 \text{ inches.}\]`

The length of DB in trapezoid ABCD is 7 inches, determined using the Pythagorean theorem.

Step-by-step explanation:

In trapezoid ABCD, with AB parallel to CD and ∠MZA being a right angle, we can use the Pythagorean theorem to find the length of DB. Considering the right-angled triangle DZA, where AD is 8 inches and DC is 9 inches, we can calculate the length of DB.

Applying the Pythagorean theorem:

`\[DB^2 = DZ^2 + ZA^2\]`

`\[DB^2 = DC^2 + AD^2\]`

`\[DB^2 = 9^2 + 8^2\]`

`\[DB^2 = 81 + 64\]`

`\[DB^2 = 145\]`

`\[DB = √(145)\]`

After evaluating, we find that DB is equal to 7 inches.