If in a parallelogram, its diagonals bisect each other right angle and are equal, then it is a

(a)Square (b)Rectangle (c)Rhombus (d)Kite

The parallelogram is a "Square" ⇒ (a)

Step-by-step explanation:

In a parallelogram

∵ In a parallelogram, its diagonals bisect each other at right angles

∴ Its diagonals are perpendicular

∵ Its diagonals are equal

→ By using rule 3 above

∴ The parallelogram is a square

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4