Question

i need all the questions and where is says to explain I need you to explain, it's pythagorean theorem, plsssss help me

Answer 1

1. option b : 10.8 miles

2. Distance = 10.2 units

Distance in miles = 20.4 miles

3. Paulie is correct because the measurements satisfies Pythagoras theorem.

Explanation:

1. option b

Let straight line length be x

x² = 6² + 9²

= 36 + 81

= 117

x = 10.8 miles

2.

Current location ( 4 , 12 )

Destination ( 6, 2 )

a)

`Distance = √((x_2 - x_1)^2 + (y_2 - y_1)^2) \\\\`

`= √((4 - 6)^2 + (12 - 2)^2) \\\\= √(2^2 + 10^2)\\\\=√(104)\\\\=10.2 \ units`

b)

Grid (units) Distance( miles)

1 2

10.2 x

`(1)/(10.2) = (2)/(x)\\\\x = 2 * 10.2\\x = 20.4 \ miles`

3.

a)

Square of Longer side = sum of squares of other sides

`17^2 = 8 ^2 + 15^2 \\289 = 64 + 225\\289 = 289 \\`

Yes, Paulie is Correct.

b)

Paulie is correct because the measurements of the sides of triangle satisfies Pythagoras theorem.

Pythagoras' theorem states that for all right-angled triangles, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

Answer 2

Explanation:

sams house=6 miles east and 9 mies south

let the distance towards east be a and distance towards south be b

so we have to find straight line distance from sams house to amys house .let it be c(or hypotenuse)

according to the pythagors theorem

a^2 + b^2 =c^2

6^2 + 9^2 =c^2

36 + 91 =c^2

117 =c^2

`\sqrt{117` =c

10.8=c

the two coordinate points are

(4,12)=(x1 , y1)

(6,2)=(x2 , y2)

distance formula =
`√((x2 - x1)^2 + (y2 - y1)^2)`

=
`√((6-4)^2 + (2-12)^2)`

=
`√(2^2 + (-10)^2)`

=
`√(4 + 100)`

=
`√(104)`

=2
`√(26)`

=10.1 units

fairy travels=10.1 * 2

=20.2 miles

three sides are 17,8,15

according to the pythagoras theorem

to be right angles triangle square of hypotenuse(longest side) must equal to the sum of square of two other smaller sides

so here 17 is longest and 8 and 15 are two other smaller sides of a triangle

17^2=8^2 + 15^2

289=64 + 225

289=289

since both sides are equal it can be concluded that they form a right angled triangle.

Hope this helps u!!