Can someone solve this for me and tell me the answer

BARSIC [14]

Answer:

A.) The greatest possible distance between any of the stakes is 53 feet.

B.) A triangle with sides 15, 36, and 39 is a right triangle and has perimeter 90 feet.

Step-by-step explanation:

Given - Fiona wants to rope off a triangular region in her yard for a vegetable garden. She has 90 feet of rope to use, she wants the distance between each stake to be an integer, and the distance between two of the stakes must be 36 feet.

To find - A. What is the greatest possible distance between any of the stakes?

B. If she wants to create a right triangular region and use all of the 90 feet of rope, what would be the lengths of the sides of the region?

Solution -

A.)

Let us assume that,

Length of side 1 = x

Length of side 2 = y

Length of side 3 = z

Now,

Given that,

She has 90 feet of rope to use

⇒x + y + z = 90

And

The distance between two of the stakes must be 36 feet.

So, Let z = 36.

∴ we get

x + y + 36 = 90

⇒x + y = 90 - 36

⇒x + y = 54

Now,

Let x be as large as possible.

i.e. To make x to be large, y has to be as small as possible.

It happens when y = 1.

( We can not take y = 0, or else a triangle won't form)

∴ we get

y = 1

⇒x + 1 = 54

⇒x = 54 - 1

⇒x = 53

∴ we get

The greatest possible distance between any of the stakes is 53 feet.

B.)

We know that,

(5,12,13) is a Pythagorean triple.

Because 5² + 12² = 13²

So,

As, we have a Pythagorean triple,

This means a triangle with sides 5, 12, 13 is a right triangle.

Now,

If a triangle has sides 5, 12, 13,

⇒ The perimeter becomes 5 + 12 + 13 = 30.

By Triple each side we get,

Length of sides 15, 36, 39.

The perimeter i= 15 + 36 + 39 = 90

Also,

We can see that,

15² + 36² = 39².

This means we have a right triangle and (15, 36, 39) is another Pythagorean triple.

Because any scaled version of a Pythagorean triple, is also a Pythagorean triple.

∴ we get

A triangle with sides 15, 36, and 39 is a right triangle and has perimeter 90 feet.

6 0

3 years ago

HELP MEEEE PLEASE!!!

Zielflug [23.3K]

Answer:

the last option

Step-by-step explanation:

test with point (1,6):

x=1 and y=6

4x + 5y - 34 = 0

4(1) + 5(6) - 34 = 0

0 = 0

test with point (6,2)

x=6 and y=2

4x + 5y - 34 = 0

4(6) + 5(2) - 34 = 0

0 = 0

6 0

4 years ago

Find the lengths of the sides of the triangle PQR. P(2, −3, −4), Q(8, 0, 2), R(11, −6, −4) |PQ| = Incorrect: Your answer is inco

Aloiza [94]

Answer:

the length PQ is 9 units,the length QR is 9 units,the length PR is 9.48 units,the triangle is not a right triangle,this is a isosceles triangle

Step-by-step explanation:

Hello, I think I can help you with this

If you know two points, the distance between then its given by:

$P1(x_{1},y_{1},z_{1} ) \\P2(x_{2},y_{2},z_{2})\\\\d=\sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1} )^{2}+(z_{2}-z_{1} )^{2} }$

Step 1

use the formula to find the length PQ

Let

P1=P=P(2, −3, −4)

P2=Q=Q(8, 0, 2)

$d=\sqrt{(8-2)^{2} +(0-(-3))^{2}+(2-(-4))^{2}} \\ d=\sqrt{(6)^{2} +(3)^{2}+(6 )^{2}}} \\d=\sqrt{36+9+36}\\d=\sqrt{81} \\d=9\\$

the length PQ is 9 units

Step 2

use the formula to find the length QR

Let

P1=Q=Q(8, 0, 2)

P2=R= R(11, −6, −4)

$d=\sqrt{(11-8)^{2} +(6-0))^{2}+(-4-2 )^{2}} \\\\\\d=\sqrt{(3)^{2} +(6)^{2}+(-6 )^{2}}} \\d=\sqrt{9+36+36}\\d=\sqrt{81} \\d=9\\$

the length QR is 9 units

Step 3

use the formula to find the length PR

Let

P1=P(2, −3, −4)

P2=R= R(11, −6, −4)

$d=\sqrt{(11-2)^{2} +(-6-(-3)))^{2}+(-4-4 )^{2}} \\\\\\d=\sqrt{(9)^{2} +(-6+3)^{2}+(-4-(-4) )^{2}}} \\d=\sqrt{81+9+0}\\d=\sqrt{90} \\d=9.48\\$

the length PR is 9.48 units

Step 4

is it a right triangle?

you can check this by using:

$side^{2} +side^{2}=hypotenuse ^{2}$

Let

side 1=side 2= 9

hypotenuse = 9.48

Put the values into the equation

$9^{2} +9^{2} =9.48^{2}\\ 81+81=90\\162=90,false$

Hence, the triangle is not a right triangle

Step 5

is it an isosceles triangle?

In geometry, an isosceles triangle is a type of triangle that has two sides of equal length.

Now side PQ=QR, so this is a isosceles triangle

Have a great day

3 0

3 years ago

Please help me with this one

ch4aika [34]

Solution is in the picture

Correct answer is : B

Good luck :)

8 0

3 years ago

Read 2 more answers

Help me out pleaseeee

Ghella [55]

Step-by-step explanation:

5p+11+8p-4

Hope it's help you

Have a great day<3

please make me brainliest please

3 0

3 years ago