The diagonals of a rhombus WXYZ intersect at M. If |MW| = 5cm and |MX| = 12cm, calculate its perimeter

Analyze the question: We have a rhombus WXYZ whose diagonals meet at M. We're given |MW| = 5 cm and |MX| = 12 cm, and we need the perimeter.

Concept: The diagonals of a rhombus bisect each other at right angles (90°). This splits the rhombus into four congruent right-angled triangles. Each side of the rhombus is the hypotenuse of one of these triangles.

Solution:

1. Triangle WMX has a right angle at M, with legs MW = 5 cm and MX = 12 cm.

2. Use Pythagoras' theorem to find side WX:

|WX|² = |MW|² + |MX|² |WX|² = 5² + 12² |WX|² = 25 + 144 = 169 |WX| = 13 cm

3. All four sides of a rhombus are equal, so:

Perimeter = 4 × 13 = 52 cm

Answer: The perimeter is 52 cm, which is option C.

Tip: 5-12-13 is a Pythagorean triple. Spotting triples like 3-4-5, 5-12-13, and 8-15-17 saves time in the exam. For any rhombus, remember: half-diagonals are the legs, the side is the hypotenuse, and the perimeter is 4 times the side.