SOLUTION: A regular pentagon has a perimeter of 15 mm. What is the area of a triangle that shares a base which one side of the pentagon that had a hypotenuse of 5mm.
A) 5 sq. Mm
B)6 sq.mm
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-> SOLUTION: A regular pentagon has a perimeter of 15 mm. What is the area of a triangle that shares a base which one side of the pentagon that had a hypotenuse of 5mm.
A) 5 sq. Mm
B)6 sq.mm
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Question 1141751: A regular pentagon has a perimeter of 15 mm. What is the area of a triangle that shares a base which one side of the pentagon that had a hypotenuse of 5mm.
A) 5 sq. Mm
B)6 sq.mm
C)12.5 sq mm Found 2 solutions by Edwin McCravy, ikleyn:Answer by Edwin McCravy(20065) (Show Source):
Since the pentagon is a regular pentagon, all 5 of its sides are equal, so
each side is the perimeter divided by 5, and 15 mm divided by 5 is 3 mm.
In a right triangle with a hypotenuse of 5mm and a leg of 3mm, the other
leg is
Solve that for a.
Since the triangle is a right triangle, we may consider one leg as the base
and the other leg as the height,
Substitute in that and solve for A
Edwin
Since the pentagon is regular, its side length is of its perimeter, i.e. 3 mm.
Having the hypotenuse of 5 mm, the given right angled triangle is (3-4-5) triangle; hence, its other leg is 4 mm.
Then the area of this triangle is = 6 square millimeters.
ANSWER. The answer is B).
