Question

HOPE is a rectangle.Its diagonals intersect each other at S.Find the value of x if SH = 2x + 4 and SE = 3x + 1.

Answer 1

∵ Diagonal of a rectangle bisect each other
∴ SE = SO
and SH = SP
∴ EO = 2SE
= 2 (3x + 1)
and HP = 2 SH = 2 (2x + 4)
∵ Diagonal of a rectangle are equal.
∴ EO = HP
⇒ 2(3x + 1) = 2(2x + 4)
⇒ 3x + 1 = 2x + 4
⇒ 3x – 2x = 4 – 1
⇒ x = 3