This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the problems: 3. Find the length of x in the similar triangles below. The two triangles are similar. We can set up a proportion using the lengths of their corresponding sides. Step 1: Identify corresponding sides. The vertical side of the upper triangle is 4 cm. The vertical side of the lower triangle is 1.5 cm. The horizontal side of the upper triangle is 6 cm. The horizontal side of the lower triangle is x cm. Step 2: Set up the proportion of corresponding sides. 4 cm1.5 cm = 6 cmx cm Step 3: Cross-multiply to solve for x. 4 × x = 6 × 1.5 4x = 9 Step 4: Divide by 4 to find x. x = (9)/(4) x = 2.25 The length of x is 2.25 cm. 4. Two triangles are \_\_\_\_\_\_ if one is the enlargement or other. Two triangles are similar if one is the enlargement or reduction of the other. This means their corresponding angles are equal and their corresponding sides are in proportion. The missing word is similar.