Question

E. Find the length of sides of the triangle whose vertices are A (7,4), B (-8, 6) Ć(1, -3).​

Answer 1

Length of sides of triangle are: AB = 15.13, BC = 12.72, AC = 9.21

Explanation:

We need to find the length of sides of the triangle whose vertices are A (7,4), B (-8, 6) C(1, -3).​

We have three sides of triangle AB, BC and AC

The length of side can be calculated using distance formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Now finding lengths of sides AB, BC and AC

i) Length of side AB

We have A (7,4), B (-8, 6)

and
`x_1=7, y_1=4, x_2=-8, y_2=6`

Putting values in formula and finding length

`Length \ of \ side \ AB \ =√((x_2-x_1)^2+(y_2-y_1)^2)\\Length \ of \ side \ AB \ =√((-8-7)^2+(6-4)^2)\\Length \ of \ side \ AB \ =√((-15)^2+(2)^2)\\Length \ of \ side \ AB \ =√(225+4)\\Length \ of \ side \ AB \ =√(229)\\Length \ of \ side \ AB \ =15.13`

So, Length of side AB is 15.13

ii) Length of side BC

We have B (-8, 6) and C(1, -3)

and
`x_1=-8, y_1=6, x_2=1, y_2=-3`

Putting values in formula and finding length

`Length \ of \ side \ BC \ =√((x_2-x_1)^2+(y_2-y_1)^2)\\Length \ of \ side \ BC \ =√((1-(-8))^2+(-3-6)^2)\\Length \ of \ side \ BC \ =√((1+8)^2+(-9)^2)\\Length \ of \ side \ BC \ =√((9)^2+(-9)^2)\\Length \ of \ side \ BC \ =√(81+81)\\Length \ of \ side \ BC \ =√(162)\\Length \ of \ side \ BC \ =12.72`

So, Length of side BC is 12.72

iii) Length of side AC

We have A (7,4)and C(1, -3)

and
`x_1=7, y_1=4, x_2=1, y_2=-3`

Putting values in formula and finding length

`Length \ of \ side \ AC \ =√((x_2-x_1)^2+(y_2-y_1)^2)\\Length \ of \ side \ AC \ =√((1-7)^2+(-3-4)^2)\\Length \ of \ side \ AC \ =√((-6)^2+(-7)^2)\\Length \ of \ side \ AC \ =√(36+49)\\Length \ of \ side \ AC \ =√(85)\\Length \ of \ side \ AC \ =9.21`

So, Length of side AC is 9.21

So, length of sides of triangle are: AB = 15.13, BC = 12.72, AC = 9.21