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Gelneren [198K]
2 years ago
12

If line segment BC is considered the base of triangle ABC, what is the corresponding height of the triangle?

Mathematics
2 answers:
Tems11 [23]2 years ago
8 0
The answer is 1.6 on e2020
Leni [432]2 years ago
7 0

Answer:

1.6 units

Step-by-step explanation:

Coordinates of A : (-1,1)

Coordinates of B : (3,2)

Coordinates of C :( -1,-1)

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

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

To find length of AB

A = (x_1,y_1)=(-1,1)

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

Now substitute the values in the formula:

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

d =\sqrt{(4)^2+(1)^2}

d =\sqrt{16+1}

d =\sqrt{17}

d =4.12

Now to find length of BC

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

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

Now substitute the values in the formula:

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

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

d =\sqrt{16+9}

d =\sqrt{25}

d =5

Now to find length of AC

A = (x_1,y_1)=(-1,1)

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

Now substitute the values in the formula:

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

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

d =\sqrt{4}

d =2

Thus the sides of triangle are of length 4.12, 5 and 2

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

To calculate the area of given triangle we will use the 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 = 4.12

b=5

c=2

Substitute the values

Now substitute the values :

s = \frac{4.12+5+2}{2}

s =5.56

Area = \sqrt{5.56(5.56-4.12)(5.56-5)(5.56-2)}

Area = 3.99

Now to find the height of altitude corresponding to side BC

So, formula of area of triangle =\frac{1}{2} \times Base \times Height

Since Area = 3.99 square units

So,3.99 =\frac{1}{2} \times BC \times Height

So,3.99 =\frac{1}{2} \times 5\times Height

3.99 =2.5 \times Height

\frac{3.99}{2.5}=Height

1.596=Height

Thus the altitude corresponding to the BC is of length 1.596 unit  ≈ 1.6 units

Thus Option D is correct.

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