Show that the two shorter sides in triangle A have the same length as the two shorter sides in triangle B

Step-by-step explanation:

a). Let the unknown side of triangle A = x cm

And unknown side of triangle B = y cm

By applying Pythagoras theorem in triangle A,

13² = 12² + x²

x² = 169 - 144

x² = 25 ⇒ x = 5 cm

By applying Pythagoras theorem in triangle B,

y² = 5² + 12²

y² = 25 + 144

y = √169

y = 13 cm

Therefore, smaller sides of these triangles measure 5 cm and 12 cm and they are same in measure.

b). Since, corresponding sides of both the triangles are congruent,

By SSS property of congruence, both the triangles will be congruent.

the answer

b. they are parallel and will never intersect.

using pemdas, (order of operations) you'll see the answer is 24.