The length and range of the hypotenuse of a right triangle is 13 cm, respectively. And 30 cm. Of the triangle
Let's calculate the area
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Let the legs of the right triangle be 'a' and 'b'. Let the hypotenuse be 'h'.
Perimeter, p = a + b + h = 30 cm
p = a + b + 13 cm = 30 cm
a + b = 30 - 13 = 17 cm
a = 17 - b …………… (1)
By Pythagoras Theorem
a² + b² = h²
(17 - b)² + b² = 13² ................ From (1)
b² + 17² - 34b + b² = 169
2b² - 34b + 289 - 169 = 0
2b² - 34b + 120 = 0
b² - 17b + 60 = 0
b² - 12b - 5b + 60 = 0
b(b - 12) - 5(b - 12) = 0
(b - 12)(b - 5) = 0
b = {12, 5}
From (1)
a = 17 - 12 = 5 cm, or a = 17 - 5 = 12 cm
a = {5,12}
The right triangles is (5 cm, 12 cm, 13 cm)
Alternatively,
The given details points to a trivial Pythagorean Triple (5,12,13).
Checking, 5+12+13 = 30.
It is a scalene right triangle.
Perimeter, p = a + b + h = 30 cm
p = a + b + 13 cm = 30 cm
a + b = 30 - 13 = 17 cm
a = 17 - b …………… (1)
By Pythagoras Theorem
a² + b² = h²
(17 - b)² + b² = 13² ................ From (1)
b² + 17² - 34b + b² = 169
2b² - 34b + 289 - 169 = 0
2b² - 34b + 120 = 0
b² - 17b + 60 = 0
b² - 12b - 5b + 60 = 0
b(b - 12) - 5(b - 12) = 0
(b - 12)(b - 5) = 0
b = {12, 5}
From (1)
a = 17 - 12 = 5 cm, or a = 17 - 5 = 12 cm
a = {5,12}
The right triangles is (5 cm, 12 cm, 13 cm)
Alternatively,
The given details points to a trivial Pythagorean Triple (5,12,13).
Checking, 5+12+13 = 30.
It is a scalene right triangle.
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