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Featured 6 months ago

To find the perimeter, you need to find the distance of each side and add them up right?

So first you need to figure out the length of each side, and you can do this by plotting the corner points and assigning vectors to each side.

When you plot the points, it should look something like this:

To find a vector

Hence to calculate the vectors between

Then the length of each vector needs to be calculated. To calculate the length of vector

You can use:

Hence when we are calculating the distances of the vectors of the triangle:

Therefore the total perimeter is

Featured 5 months ago

The coordinates are

The length of side

Let the height of the triangle be

The area of the triangle is

The altitude of the triangle is

The mid-point of

The gradient of

The gradient of the altitude is

The equation of the altitude is

The circle with equation

The intersection of this circle with the altitude will give the third corner.

We solve this quadratic equation

The points are

graph{(y-1/3x-1)((x-7.5)^2+(y-3.5)^2-291.6)((x-7)^2+(y-5)^2-0.05)((x-8)^2+(y-2)^2-0.05)(y-5+3(x-7))=0 [-12, 28, -10, 10]}

Featured 3 months ago

see explanation

1) to find length

Let

Let

Consider

As

2) to find length

Featured 1 month ago

Please see below.

Let us consider the following figure, where we have the median

Now in

=

or **.....................(1)**

and in

=

or

But as

**.....................(2)**

Adding (1) and (2), we get

or

This is Apollonius theorem.

Featured 1 month ago

area

Circle 1 :

Circle 2:

As the two circles touch each other externally, they have 3 common tangents.

Obviously, Y-axis

Let

Circle 1 :

As the line

Similarly, Circle 2 :

similarly, set the discriminant

Solving

a) when

b) when

Setting

As

Featured 1 month ago

Given that

- the equation of parabola
#y=x^2# - the equation of a straight line
#y=2x-17#

Let the corner points

So **slope** of AD

Hence we have

The length of side

#=(t_1-t_2)sqrt(1+(t_1+t_2)^2)#

#=(t_1-t_2)sqrt(1+2^2)=sqrt5(t_1-t_2)=2sqrt5(t_1-1)#

Now length of the perpendicular from

We have

Hence we get

When

So

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