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What is the perimeter of a 30-60-90 triangle whose shorter leg is 5 inches long?
a. 5 3 cm c. 15 + 3 cm
b. 15 + 5 3 cm d. 10 + 5 3 cm


Sagot :

The 30-60-90 triangle theorem states that the hypotenuse is twice the measure of the shorter leg. Furthermore, the sides of this type of triangle is in the ratio 1:2:[tex] \sqrt{3} [/tex]


Hence, since the shorter leg measures 5 inches, 

hypotenuse is equal to 5(2) = 10 inches, 

and the longer leg is 5[tex] \sqrt{3} [/tex]

Then the perimeter is 5+10+5[tex] \sqrt{3} [/tex] = 15+5[tex] \sqrt{3} [/tex] 

Hence, the answer is B. 15+5[tex] \sqrt{3} [/tex] inches