**Answer:**

14 units, 19.8 units (3 s.f.)

**Step-by-step explanation:**

To find the length of each side of the square ABCD, find the length of AB.

Refer to the picture attached.

AB= AX +XB

Let's find the length AX first.

(see triangle AXY)

Applying Pythagoras' Theorem,

(AX)² + (XY)² = (AY)²

(AX)² +12²= 13² (subst. known values)

(AX)²= 169 -144 (move constant to 1 side)

(AX)²= 25 (simplify)

AX= √25 (square root both sides)

AX= 5 units

Now, let's find the length of XB.

(see triangle BXY)

Applying Pythagoras' Theorem,

(XB)² + (XY)²= (BY)²

(XB)² +12²= 15²

(XB)²= 225 -144 (bring constant to 1 side)

(XB)²= 81 (simplify)

XB= √81 (square root both sides)

XB= 9 units

AB

= 5+9

= 14 units

Therefore, length of each side of square ABCD= **1****4**** ****units**

To find the diagonal of the square, focus on the red shaded triangle (refer to picture 1).

Since squares have equal sides, AD= DC= 14 units

Applying Pythagoras' Theorem,

(AC)²= (AD)² +(DC)²

(AC)²= 14² +14² (subst. known values)

AC= √392 (simplify)

AC= **19.8**** units** (to 3 s.f.)