Question

two doorknobs have cross sections that are right triangles. see the figures below. both doorknobs have a 20° angle. for both doorknobs, the length of the side between the 90° and 20° angles is the same. (a) are the cross sections (the right triangles) congruent? yes no the cross sections are congruent by the angle - side - angle (asa) congruence property. correct answer: - yes the cross sections are congruent by the angle - side - angle (asa) congruence property. part 2 of 2 (b) if each cross section has a height of 2 inches and x = 5, what is the combined area of the two cross sections, using these values? ⅛ in²

Explanation:

Step1: Recall area of triangle

The area of a triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \). Here, each cross - section is a triangle with base \( x = 5 \) inches and height \( h=2 \) inches.

Step2: Calculate area of one cross - section

Substitute the values into the formula: \( A_{1}=\frac{1}{2}\times5\times2 \). First, multiply \( 5\times2 = 10 \), then \( \frac{1}{2}\times10=5 \) square inches. So, the area of one cross - section is 5 square inches.

Step3: Calculate combined area of two cross - sections

Since there are two congruent cross - sections, the combined area \( A = 2\times A_{1} \). Substitute \( A_{1} = 5 \) into the formula: \( A=2\times5 = 10 \) square inches.

Answer:

The combined area of the two cross - sections is \(\boldsymbol{10}\) square inches.