The 2 triangles shown are similar. Find the value of 
ab
.

Two right triangles, each hypotenuse on the same line. First triangle, horizontal side length 1 point 4, vertical side length 2 point 1. Second triangle, horizontal side length b, vertical length a.

Since the two triangles are similar, their corresponding sides are proportional. Let's set up a proportion between the corresponding sides of the two triangles to find \( a \) and \( b \).

### Step-by-Step Solution

1. **Given information**:
   - First triangle (let's call it Triangle 1):
     - Horizontal side = \( 1.4 \)
     - Vertical side = \( 2.1 \)
   - Second triangle (Triangle 2):
     - Horizontal side = \( b \)
     - Vertical side = \( a \)

2. **Proportion setup**:
   Since the triangles are similar, the ratios of the corresponding sides are equal:
   \[
   \frac{1.4}{b} = \frac{2.1}{a}
   \]

3. **Simplifying the Ratio**:
   Dividing both 2.1 and 1.4 by 0.7 gives:
   \[
   \frac{2.1}{1.4} = 1.5
   \]
   This means:
   \[
   \frac{a}{b} = 1.5
   \]

4. **Finding \( ab \)**

The 2 triangles shown are similar. Find the value of ab.

Solve for the value of ab in similar triangles by using ratios of corresponding sides. This problem explores the concept of triangle similarity, where side lengths are proportional, and applies a step-by-step approach. Suitable for students in Grades 8-10.

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