Clearly the line BD divided the triangle ABC into two identical triangles ABD and CBD.

This goes to show that lengths AD and CD are equal and lengths AB and CB are equal.

Since lengths AD and CD are equal...
...3x + 4y = 29.

Since lengths AB and CB are equal...
....4x + y = 3x + 2y - 2.

3x + 4y = 29 (Equation 1)
4x + y = 3x + 2y - 2 (Equation 2)

Let's modify equation 2 to express x in terms of y so that we can substitute the expression for x into equation 1.

From equation 2,
4x = 3x + 2y - 2 - y
4x = 3x + y - 2
4x - 3x = y - 2
x = y - 2

Our simplified equations for part (a) are 3x + 4y = 29 and x = y - 2 (or any equivalent format).

Let's substitute the x in equation 1 by the equivalent (y - 2).

In equation 1,
3x + 4y = 29
3 (y - 2) + 4y = 29
3y - 6 + 4y = 29
7y - 6 = 29
7y = 29 + 6
7y = 35
y = 5

And now for x.

x = y - 2
x = 5 - 2
x = 3

So, our answers for part (b) are x = 3 and y = 5.

Clearly when x = 3 and y = 5, the length of AB = 4(3) + 5 = 17 cm.

So, the perimeter of the triangle
= 29 + 29 + 17 + 17
= 92 cm

This question is a bad question because the length AB, being the diagonal of the right-angled triangle, should be the longest length in triangle ABD, but here it turns out that the length of AB is 17 cm and the length of AD is 29 cm.

AB < AD
wrong Q