Question

I need help please! MEDAL AND FAN. Photo will be in the comments.

1A.) Draw an right triangle inside the rectangle so that the area of the triangle is 1/4 the area of the rectangle. Position one side of the triangle along one side of the rectangle.
1B.) Explain how you know that the area of your triangle is 1/4 the area of the rectangle.

Answer 1

how you think it ? try drawing it

Answer 2

I did and I have gotten it wrong every time

Answer 3

It sounds like you're already given a drawing of a rectangle?

Answer 4

one way is to draw a right triangle where 2 of the legs lie along the rectangle sides

one leg is exactly equal to the length of the rectangle (bottom side)
the other leg of the triangle is half as long as the height

see attached to look at the red triangle I drew. This red triangle has exactly 1/4 of the area of the rectangle

Answer 5

Okay so now what to I do? @jim_thompson5910

Answer 6

that wraps up part A. You now need to explain why this works in part B

Answer 7

do you see why this works?

Answer 8

Isn't because now both parts of the rectangle are the same? @jim_thompson5910

Answer 9

if the base is x and the height is y, then what is the area of the rectangle?

Answer 10

I have am not sure...... @jim_thompson5910

Answer 11

the area would be base*height = x*y, no?

Answer 12

I'm referring to the rectangle

Answer 13

Oh I see now, so I would say use formula A=bh?

Answer 14

@jim_thompson5910

Answer 15

and the other part c, it says suppose a grain of sand randomly falls onto your drawing. What is the probability that it lands on the right triangle? @jim_thompson5910

Answer 16

so the area of the rectangle is x*y

what is the area of the triangle?
base of triangle = x
height of triangle = y/2

Answer 17

x and y are both 1/4 right?

Answer 18

@jim_thompson5910

Answer 19

no, x and y are unknowns really

Answer 20

if the base is x and the height is y/2, then we plug them into b*h/2

b*h/2 = x*y/2*(1/2) = x*y/4

agreed?

Answer 21

Okay, my partner on this assignment said they were both 1/4

Answer 22

Yes agreed

Answer 23

so the rectangle has area x*y
the red triangle has area x*y/4

Answer 24

this shows that the triangle area is 1/4 of the rectangle area

Answer 25

Okay now I get it thank you. And did you see the part c up a ways in the comments

Answer 26

`and the other part c, it says suppose a grain of sand randomly falls onto your drawing. What is the probability that it lands on the right triangle? `

the triangle has 1/4 of the area of the rectangle, so the chances of it landing in the triangle is 1/4 = 0.25 = 25%

Answer 27

if you want hard numbers, then say the rectangle is 20 by 5

base = 5
height = 20

area of rectangle = 5*20 = 100 square units

the triangle would be 10*5/2 = 50/2 = 25 square units

25/100 = 1/4 is the probability of landing on the triangle

Answer 28

Thank you so much! could you help me with the other parts please?

Answer 29

which other part?