Answer:
14 units, 19.8 units (3 s.f.)
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= 14 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.)