Math, asked by harshchaudhry4946, 1 year ago

The vertices of a triangle are (-2,0), (2,3) and(1,-3) .Is the triangle equilateral isosceles or scalene?Also find the area of the triangle

Answers

Answered by fadkeabhi1
5
scalele triangle

Area will be 10.5 units
Answered by wifilethbridge
8

Answer:

Scalene triangle

Area = 10.49 square units

Step-by-step explanation:

The vertices of triangle are (-2,0), (2,3) and(1,-3)

Let Point A = (-2,0)

Point B = (2,3)

Point C = (1,-3)

Now to find sides of triangle we will use distance formula :

d =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Now find the length of AB

So, A = (x_1,y_1)= (-2,0)

B = (x_2,y_2)= (2,3)

Substitute the values

d =\sqrt{(2-(-2))^2+(3-0)^2}

d =\sqrt{(4)^2+(3)^2}

d =\sqrt{16+9}

d =\sqrt{25}

d =5

So, AB = 5 units

Now to find BC

B = (x_1,y_1)= (2,3)

C = (x_2,y_2)= (1,-3)

Substitute the values

d =\sqrt{(1-2)^2+(-3-3)^2}

d =\sqrt{(1)^2+(-6)^2}

d =\sqrt{1+36}

d =\sqrt{37}

d =6.08

BC = 6.08 units

To Find AC

A = (x_1,y_1)= (-2,0)

C = (x_2,y_2)= (1,-3)

Substitute the values

d =\sqrt{(1-(-2))^2+(-3-0)^2}

d =\sqrt{(3)^2+(-3)^2}

d =\sqrt{9+9}

d =\sqrt{18}

d =4.24

AC = 4.24 units

So, the sides of the triangle are 5 units , 6.08 units and 4.24 units

Since all the side are of unequal length

So, the triangle is scalene triangle

Now to find area of triangle we will use heron's formula:

Area = \sqrt{s(s-a)(s-b)(s-c)}

Where s = \frac{a+b+c}{2}

a,b,c are the side lengths of triangle  

a =5

b=6.08

c = 4.24

Now substitute the values :

s = \frac{5+6.08+4.24}{2}

s =7.66

Area = \sqrt{7.66(7.66-5)(7.66-6.08)(7.66-4.24)}

Area = 10.49

Hence the area of the triangle is 10.49 square units

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