Math  /  Geometry

QuestionThe end views of two different barns are shown. Without calculating, decide which end has the greater area. Explain how you know
Choose the correct answer below. A. The end of Barn 1 has a greater area because the rectangular part has a greater width than that of the rectangular part of the end of Barn 2 , while they both have the same length. B. The end of Barn 1 has a greater area because the triangular part has a greater height than that of the triangular part of the end of Barn 2 , while they both have the same base. C. The end of Barn 2 has a greater area because it has the longest vertical side, though Barn 1 is taller. D. The end of Barn 2 has a greater area because both the triangular and rectangular parts have greater areas than the corresponding parts for Barn 1 .

Studdy Solution

STEP 1

1. Both barns have a rectangular section and a triangular section.
2. The rectangular sections of both barns have the same height of 90.
3. The triangular section of Barn 1 has a height of 75.
4. The triangular section of Barn 2 has a height of 60.
5. Both barns have the same base width.

STEP 2

1. Compare the rectangular sections.
2. Compare the triangular sections.
3. Determine which barn end has the greater area.

STEP 3

Compare the rectangular sections:
Since both barns have the same rectangular height and base width, the areas of the rectangular sections are equal.

STEP 4

Compare the triangular sections:
Barn 1 has a triangular height of 75, while Barn 2 has a triangular height of 60. Since both triangles have the same base width, the area of the triangular section of Barn 1 is greater.

STEP 5

Determine which barn end has the greater area:
Since the rectangular sections are equal and the triangular section of Barn 1 is greater, Barn 1 has the greater total area.
The correct answer is:
B. The end of Barn 1 has a greater area because the triangular part has a greater height than that of the triangular part of the end of Barn 2, while they both have the same base.

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