The first step is to section the given daigram. It would be shown in the diagram below
Looking at the diagram,
Area of family room = 5.5 * 24 = 132 square feet
Area of hallway = 15.5 * 4 = 62 square feet
Total area to be covered with carpet is
132 + 62 = 194 square feet
Since the cost per square foot is $4, then the cost of putting carpet in the family room and hallway is
194 * 4 = $776* 4 = $776
Based on the above, the Triangle XYZ and ACB are known to be similar triangles since tanX = tanA = 5 over 2 and 5 tenths;
Hence:
From the question given; Triangle XYZ is known to have been dilated by a scale factor of 2 to form a type of triangle known as triangle ACB, So therefore, XYZ and ACB are known to be the same or similar triangles.
Since Angles Y and C are known to both measure 90 degrees, and angles A and X are said to be congruent. Therefore:
tanX = tanA = 5 over 2 and 5 tenths
AC = 2 x XY
CB = 2 x YZ
For part B:
cosX=Base/Hypotenuse
cos A=AC/AB
AC = 2.05
AB = 5.59
Therefore, Based on the above, the Triangle XYZ and ACB are known to be similar triangles since tanX = tanA = 5 over 2 and 5 tenths;
Hence:
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