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Step-by-step explanation:
In triangle ABC, angle B is 90, BC is 80cm, and AC is 100cm. BD divides the triangle in two equal perimeters. What is BD?
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In the given right triangle ABC , hypotenuse AC is 100 cm and BC, say base is 80 cm so height AB is
√(100^2 - 80^2 ) cm or 60 cm
As given , let the given line BD, D on AC be x cm dividing the triangle ABC into two triangles ABD and BCD having equal perimeter.
Let CD is y cm and so AC is 100-y cm
As perimeters of ABD and BCD are equal :
x + 60 + 100-y = x + 80 + y ….. (1)
Or, 160 - y = 80+y , or
2y = 160–80 = 80
So, y (CD) = 80/2 or 40 cm
Thus AD = 100–40 or 60 cm .
Now we know the sides of ABC as 60, 80 and 100.
Let us consider angle BAC as z , so angle ACB is 180° - 90° - z or 90-z
Now let us use property of triangle's sides Vs opposite angles when we get relationship as follows :
90/100 = z/80 = (90-z)/ 60
So, z ( angle BAC) = 80* 90/100 = 72°
Now as AB = AD = 60 , triangle ABD is isosceles and so angle ABD = ADB = (180–72)/2 = 54°
Now let use the same property of angle Vs sides for triangle ABD when we get :
60/54 = x (BD) /72 , or BD (x) = 72* 60/54 = 80
So measure of BD bisecting triangle ABC into two triangles with equal perimere is 80 cm.
(angle ACB = 180–90–72 = 18°) .. redundant
Answer:
In triangle ABC, angle B is 90, BC is 80cm, and AC is 100cm. BD divides the triangle in two equal perimeters. What is BD?
Your newborn may be vulnerable to these 6 serious diseases.
In the given right triangle ABC , hypotenuse AC is 100 cm and BC, say base is 80 cm so height AB is
√(100^2 - 80^2 ) cm or 60 cm3
As given , let the given line BD, D on AC be x cm dividing the triangle ABC into two triangles ABD and BCD having equal perimeter.
Let CD is y cm and so AC is 100-y cm
As perimeters of ABD and BCD are equal :
x + 60 + 100-y = x + 80 + y ….. (1)
Or, 160 - y = 80+y , or
2y = 160–80 = 80
So, y (CD) = 80/2 or 40 cm
Thus AD = 100–40 or 60 cm .
Now we know the sides of ABC as 60, 80 and 100.
Let us consider angle BAC as z , so angle ACB is 180° - 90° - z or 90-z
Now let us use property of triangle's sides Vs opposite angles when we get relationship as follows :
90/100 = z/80 = (90-z)/ 60
So, z ( angle BAC) = 80* 90/100 = 72°
Now as AB = AD = 60 , triangle ABD is isosceles and so angle ABD = ADB = (180–72)/2 = 54°
Now let use the same property of angle Vs sides for triangle ABD when we get :
60/54 = x (BD) /72 , or BD (x) = 72* 60/54 = 80
So measure of BD bisecting triangle ABC into two triangles with equal perimere is 80 cm.
(angle ACB = 180–90–72 = 18°) .. redundant
Step-by-step explanation:
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