Question

what is the perimeter of the larger triangle?
36 units
12 units
24 units
3 units

Explanation:

Step1: Check Similar Triangles

The two triangles are similar (same angles, right triangles with a common acute angle). The ratio of corresponding sides: smaller triangle base \(3\), larger base \(9\), so scale factor \(k = \frac{9}{3}=3\).

Step2: Find Larger Triangle's Height

Smaller height is \(4\), so larger height \(= 4\times3 = 12\).

Step3: Calculate Perimeter of Larger Triangle

Larger triangle sides: \(9\) (base), \(12\) (height), \(15\) (hypotenuse). Perimeter \(= 9 + 12 + 15 = 36\).

Answer:

36 units