swerve wrote:Patricia builds two triangles, each with 30 feet of wood. The first triangle ABC is built to maximize the length of the base side. The second triangle DEF is built to maximize the area of the triangle. What is the ratio of the length of the base of triangle ABC to the length of the base of triangle DEF? The lengths of all line segments are integers.
A. 1:1
B. 6:5
C. 5:4
D. 7:5
E. 2:1
The OA is D
Source: Veritas Prep
So, we have two triangles with the perimeter 30 feet given that the sides of the triangles are integers.
1. Triangle-1 has the maximum possible base:
The maximum possible base would be a little less than half the perimeter of the triangle.
Thus, the maximum possible base < 1/2 of 30 (= 15)
The maximum possible base or base of ∆ABC = 14 since it is given that the sides of the triangles are integers.
1. Triangle-2 has the maximum possible area:
For the given perimeter 30, the maximum possible area would be for a triangle that has the same sides; thus, it is an equilateral triangle.
Thus, side of an equilateral triangle of ∆DFF = 30/3 = 10 feet
Ratio of the length of the base of triangle ABC to the length of the base of triangle DEF = 14/10 = 7 : 5.
The correct answer:
D
Hope this helps!
-Jay
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