Question

Figure ABCD is a rectangle. The length of segment AE is (5x - 7) units and the length of segment EC is (2x - 1) units.

Rectangle ABCD with point E as the point of intersection of the two diagonals. The length of AE is labeled (5x – 7) and the length of EC is labeled (2x - 1).

What is the length of diagonal BD?

8 units

6 units

12 units

10 units

Answer 1

the point of intersection of diagonal in rectangle divides each diagonal into two equal parts, so you just need to solve for x
\[5x-7 = 2x-1\]

we find x = 2, the substituting x into the equation and adding the two parts to get the length of the diagonal would give :
6