Question

Find the perimeter of the triangle defined by the coordinates (7, 1), (-6, 1), and (10, 6). (Round to nearest tenth)

Answer 1

`35.6\ units`

Explanation:

we know that

The perimeter of triangle is equal to the sum of the length of the three sides

Let

`A(7, 1), B(-6, 1), C(10, 6)`

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

Find the distance AB

`A(7, 1), B(-6, 1)`

substitute in the formula

`d=\sqrt{(1-1)^(2)+(-6-7)^(2)}`

`d=\sqrt{(0)^(2)+(-13)^(2)}`

`dAB=13\ units`

Find the distance BC

`B(-6, 1), C(10, 6)`

substitute in the formula

`d=\sqrt{(6-1)^(2)+(10+6)^(2)}`

`d=\sqrt{(5)^(2)+(16)^(2)}`

`dBC=16.8\ units`

Find the distance AC

`A(7, 1), C(10, 6)`

substitute in the formula

`d=\sqrt{(6-1)^(2)+(10-7)^(2)}`

`d=\sqrt{(5)^(2)+(3)^(2)}`

`dAC=5.8\ units`

Find the perimeter

`P=dAB+dBC+dAC`

`P=13+16.8+5.8=35.6\ units`