A right triangle has angles which measures 30° ,60°,90° if the perimeter of this triangle is 15+5√3 then the length of the hypotenuse of this triangle
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Let
AB = x
Tan C = AB/BC
Tan 30° = x/BC
1/√3 = x/BC
BC = √3 *x
Similarly by using Sin C we get AC = 2x
Now
perimeter = x + √3*x + 2x
15+5√3 = 3x + √3*x (given)
(3+ √3)*5 = (3 + √3)*x
x = 5
Now
Hypotenuse = 2x = 10 Ans
AB = x
Tan C = AB/BC
Tan 30° = x/BC
1/√3 = x/BC
BC = √3 *x
Similarly by using Sin C we get AC = 2x
Now
perimeter = x + √3*x + 2x
15+5√3 = 3x + √3*x (given)
(3+ √3)*5 = (3 + √3)*x
x = 5
Now
Hypotenuse = 2x = 10 Ans
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