Question

julio considers the reduction of the triangle.
image of two triangles: pink triangle with height 12 in, base 21 in; blue triangle with height 8 in, base x in. text: not drawn to scale
what is the correct cross product that he should use to solve for the missing dimension?
options:
(8)(12) = 21x
(8)(21) = 12x
(12)(8) = 12x
(12)(21) = 8x

Explanation:

Step1: Identify Similar Triangles

The two triangles are similar (reduction implies similarity), so their corresponding sides are proportional. The ratio of the heights is \(\frac{8}{12}\) and the ratio of the bases is \(\frac{x}{21}\).

Step2: Set Up Proportion

For similar triangles, \(\frac{8}{12}=\frac{x}{21}\).

Step3: Cross - Multiply

Cross - multiplying gives \(8\times21 = 12\times x\), which is \((8)(21)=12x\).

Answer:

B. \((8)(21) = 12x\)