Question

each of the 2 equal side of the triangle is half the 3rd side if perimeter of triangle is 100 cm find the sides of the traingle​

Answer 1

Answer:

Poligon: triangle equilateral ABC

base AB = 10 cm

oblique side BC = 10 cm

I calculate half base knowing that:

base = 10 cm

divisor = 2

I apply the formula:

half base =  and I get:

half base =  = 5 cm

Reply

half base it is 5 cm

Data

Poligon: right triangle HBC

cathetus c = HB = 5 cm

hypotenuse a = BC = 10 cm

Solution

It requires the cathetus of a right triangle HBC having:

cathetus c = HB = half base = 5 cm

hypotenuse a = BC = oblique side = 10 cm

I apply the formula derived from the Pythagorean theorem:

cathetus b = CH = height = V a² - c² and I get:

cathetus b = V(10 cm)² - (5 cm)² = 8,6602540378444 cm

Reply

The other cathetus b = CH of the right triangle HBC, which coincides with the height, is 8,6602540378444 cm.

Data:

Poligon: triangle equilateral ABC

base b = AB = 10 cm

height h = CH = 8,6602540378444 cm

Solution

I calculate the area of triangle equilateral ABC having:

base b = AB = 10 cm

height h = CH = 8,6602540378444 cm

I apply the formula A =  and I get:

A =  = 43,301270189222 cm²

Reply

The area of triangle equilateral ABC is 43,301270189222 cm²

Data:

Poligon: triangle ABC

AB = 10 cm

BC = 10 cm

CA = 10 cm

Solution

It requires the perimeter of the triangle ABC whose sides are:

AB = 10 cm

BC = 10 cm

CA = 10 cm

I apply the formula:

p = AB + BC + CA

and I get:

p = 10 cm + 10 cm + 10 cm = 30 cm

Reply

The perimeter of triangle ABC is 30 cm

Time taken to resolve the problem: 0 seconds

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Answer 2

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In the Isosceles Triangle ABC,

∠BAC = 30°

So,

∠CBA also = 30° = x (Opposite side in a Isosceles ∆)

_____________________________________

If ∠BAC & ∠CBA = 30°

Then,

∠BAC + ∠CBA + ∠ACB = 180° (Angle Sum Prop. of a Triangle)

➠ 30° + 30° + ∠ACB = 180°

➠ ∠ACB = 180° - 60°

➠ ∠ACB = 120°

If ACB = 120° Then,

∠BCD = 180° - 120°

∠BCD = z = 60°

___________________________________

If z = 60°

Then,

Y also = 60° (Opp. Sides in an Isosceles ∆ )

____________________________________

Overall,

x = 30°

y = 60°

z = 60°

.

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