814 Math Blog (2011): January 2012

Sheila's Textbook Questions

A) Alex is thinking of the number 60.

B) No, there is only one answer. The number must be between 40 and 64. The only multiple of 12 in the range 60.

16) A fitness center will install a square hot tub in a 6m x 6m room. They want the tub to fill no more than 75% of the room area.

A) What is the maximum area of the hot tub ?

27m2

B) What dimensions , to the tenth of a meter , will the fitness center order from the manufacturer? Explain.

The fitness center should get a 5.1m by 5.1m so that it doesn't go over the available space.

Here is a link of square roots.

Sorry i couldn't get the video up so here's a link instead.

ENJOY!

1. The relationship between the lengths of the sides of a right triangle. The sum of the areas of the squares attached to the legs of a right triangle equals the area of the square attached to the hypotenuse3232. a + b = c

2.Solve the missing side lenght.

3. Is this a right triangle? Prove it.

Raeesa's Square Root Answers #-5,12,and 17

17)a,b,c

12) a,b,c.

c- yes because the side lengths of the rug is shorter than both side lengths of the room.

5) a,b,c.

http://www.youtube.com/watch?v=iGJzW7iC5no&feature=related

This Pythagorean Relationship means that the sum of the areas of the two shortest sides of a right angle triangle (a and b) must always be equal to the area of the hypotenuse (c).

2) Solve for the missing side length.

a^2+b^2=c^2

12^2+ 5^2= c^2

144+ 25= c^2

169=c^2

root 169= root of c

13cm = c

the hypotenuse equals to 13cm.

3) Is this a right triangle? Prove it!!!

a^2 +b^2= c^2

8cm^2+6cm^2= 11cm^2

(8 times 8) + (6 times 6)= ( 11 times 11)

64+ 36=121

100 =/121

No, this is not a perfect right triangle because a^2 + b^2 is not equal to c^2.

Kassey's Textbook Questions

4. Estimate the square root for each number, to one decimal place. check with a calculator.

Estimate: A) 8.4 B) 10.2 C) 7.3

Calculations: A) 8.4 B) 10.1 C) 7.2

16. A fitness room center will install a square hot tub in a 6m x 6m room. They want the tub to fill no more than 75% of the rooms area.

A) what is the maximum area of the hot tub?

B) what dimensions to a tenth of a meter will the fitness center order from the manufacturer? Explain.

9) what are all the possible whole numbers that have a square root between 4 and 5?

A: 17, 18, 19, 20, 21, 22, 23, 24

Here is a video for square and square roots:

Pythagoras:

1) Explain the Pythagoras Relationship:
The relationship between the lengths of the sides of a right triangle. The sum of the area of the squares attached to the legs of a right triangle equals the area of the square attached to the hypotenuse.

2) What is the missing length?

It is 13cm because the hypotenuse ( or C ) has to be a larger

number than the legs ( or A, B ).

3) Is this a right triangle ?
This is not a right triangle because a square + b square does not = c square also the legs added together does not equal the hypotenuse.

Aaron's textbook questions

a) The area of the picture is 324cm squared, because 18cm x 18 = 324'

b) The area of the board is 1296 cm squared, 324x4 = 1296

c) The dimensions of the board is 36 cm by 36 cm, because the square root of 1296 is 36.

The order of the numbers is √27, 5.8, 6.3,√46 , 7. 27 is first because √27= 5.1 which is smaller than 5.8. 5.8 is second because 6.3 is higher than 5.8. 6.3 is third because √46= 6.7 which is higher than 6.3. √46 is fourth because its higher than 6.3, √46= 6.7. 7 is last because all the other numbers are lower than it and no other number is higher than it.

a) the maximum area of the hot tub is 27m squared because 25% of 36 is 9 and 9x3 = 27 which is 75%.

b) the fitness center should order 5.1m by 5.1m because √27 = 5.1 , and they cant go over 75% of their space.

Here is a video to help you

www.youtube.com/watch?v=NNHlnh7AURM

Irena's Textbook Questions

Here's a link on square roots.

Here's a video on square roots.

1. Answer in a short paragraph and with diagrams.

Pythagorean Relationship:

The relationship between the lengths of the sides of a right triangle. The sum of the areas of the squares attached to the legs of a right triangle equals the area of the square attached to the hypotenuse. 2 2 2

a + b = c

2. Solve the missing side length

3. Is this a right triangle? Prove it!

No it is not a right triangle. It is not a right triangle because the sum of the areas of the squares of the legs are not equal to the area of the square of the hypotenuse.