Two similar triangles, Triangle X and Triangle Y, have perimeters of 24 cm and 36 cm, respectively. If the area of Triangle X is 40 cm², what is the area of Triangle Y?
Show answer & explanation
Correct answer: C
Explanation
Given:
Perimeter of triangle x = 24 cm
Perimeter of triangle y = 36 cm
Area of triangle x = 40 cm²
By the formula:
In similar triangles
Ratio of areas = (Ratio of sides)²
Ratio of sides = 36 : 24 = 3 : 2
Ratio of areas = (3/2)² = 9/4
Area of triangle y = 40 × 9/4 = 90 cm²