Resultant Acceleration of an Object Under Perpendicular Forces

[Jamotron]

A simple problem from a list of many I was working through as revision:

Homework Statement

Two ropes are attached to a 40kg object. The first rope applies a force of 45 N, and the seond 40 N. If the two ropes are perpendicular to each other, what is the resultant acceleration?
a)1.2m/s²
b)3.0m/s²
c)25m/s²
d)47m/s²

Homework Equations

F=ma
F_1x=F₁cos theta₁
F_2x=F₂cos theta₂

F_1y=F₁sin theta₁
F_2y=F₂sin theta₂

a=(a_x²+a_y²)^1/2

The Attempt at a Solution

As the angles of ropes to the object are not given but the ropes are stated as being perpendicular I took 45 degrees as the angle of both ropes, which gives me the same answer for F_x and F_y which is49.45N. Therefore:
a_x=F_x/M = 1.23m/s²
a_y=F_y/M=1.23m/s²
Now, this value is consistent with answer a) given in the question. However I was under the impression that to find the magnitude of the acceleration I need to use the equation
a=(a_x²+a_y²)^1/2. As I've figured the x and y acceleration to be equal this will give me a =1.74 m/s².

So where have I gone wrong? What would be the correct procedure for solving this problem? I'm very new to physics so any help would be appreciated :)

 

[Jamotron]

Anybody out there able to help at all?

 

[ashishsinghal]

It does not matter what angle you are considering as the magnitude of acceleration will be same (if no other force such as gravity are being considered). Hence just use Pythagoras theorem.

And do not be impatient. Members here are able to solve question much more difficult than this. Do not question the ability, in future.