American Math rejecto! Needs help again..?

Question

1)The length of the three sides of a right triangle are consecutive even integers find them.




2) How high on a building will a 15-foot ladder touch if the foot of the ladder is 5 feet from the building?


Help, please, im bad at geometry, please help, im confused took my 2hours on these!!

Answer 1

For question 1..

It is rather known that the three sides having 3cm,4cm and 5cm (the hypothenus) are length of a right angled triangle. Using the pythagoras theorem, 3^2+4^2 = 5^2. In order to have consecutive even integers, we can mutiply 3, 4, 5 by 2. And we get 6,8,10. Check if it will work out as a right angled triangle. Use the pythagoras theorem, 6^2 + 8^2 =100 which is equals to 10^2. So the three consecutive even integers are 6, 8, 10.


For question 2...

Draw a right angled triangle to represent. Let the height of the building be a The length of the ladder will be the hypothenus. Using the pythagoras theorem, a^2 + 5^2 =15^2. To find a^2, 15^2-5^2 = a^2 which is 200. Then you square root 200 to get a which will be 14.14.

I hope it helped. Good luck!

Answer 2

We know that 3, 4, and 5 are consecutive integers and that they are exact sides of a right triangle. Multiply each by 2 to get three consecutive even integers which are sides of a right triangle.

2) Again the Pythagorean Theorem,
c^2 - a^2 = b^2
b^2 = (15^2 - 5^2)

Answer 3

for two 5^2+x^2=15^2 so x^2=200 so x=the square root of 200 or 10 to the square root of 2 im pretty sure those answers are correct! but double check

and one should be 6, 8, 10.. i just started plugging #s in pythag even ones that wereconsecutive.

agin, double check, but I hope this helps!

for the question above mine, 14 squared is 196 not 200

Answer 4

the first one is 3,4,5

itz the pythagoreum theorum < i probably spelled that wrong

but anyway thats it and the next one you could use the same thing. the pythagorem theorum.

a squared + b squared= c squared

so 5 squared or 25 + b squared= 15 squared or 225

fill in the blank.

sry i dont have a calculator w/ me.

hope this helpz.

Answer 5

14.142135623730950488016887242097 feet.