2022 · Q92
X, Y and Z are three equilateral triangles. The sum of the areas of X and Y is equal to the area of Z. If the side lengths of X and Y are 6 cm and 8 cm respectively, then what is the side length of Z?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A9 cm
- B9.5 cm
- C10 cm
- D10.5 cm
Explanation
Areas give (√3/4)(36+64) = (√3/4)z², so z² = 100 and z = 10 cm. Since area scales as the square of the side, the areas add like Pythagoras: 6²+8² = z². The keyed option is C.