$1$ added to the product of two consecutive even numbers gives $289$. What are the numbers?

$9$ added to the product of two consecutive multiples of $6$ gives $729$. What are the numbers?

How many terms of the arithmetic sequence $5,7,9,...,$ must be added to get $140$?

$16$ added to the sum of the first few terms of the arithmetic sequence $9, 11, 13,....$ gave $256$. How many terms were added?

An isosceles triangle has to be made like this. The height should be $2$ meters less than the base and the area of the triangle should be $12$ square meters. What should be the length of its sides?

A $2.6$ metre long rod leans against a wall, its foot $1$ metre from the wall. When the foot is moved a little away from the wall, its upper end slides the same length down. How much farther is the foot moved from the wall?