I really need help!!!
Lars stretched 12 yards of a string from stake X to stake Y and 9 yards of the string from stake Y to stake Z. The two strings meet at a right angle.
He wants to stretch the string from stake Z to stake X next. What is the distance from stake Z to stake X?
A.15 yards
B.21 yards
C.113 yards
D.3 yards
thank you so much!
i got a couple more qushtions can you stay and help me?
You are welcome.
The Pythagorean Theorem to the rescue!
a^2 + b^2 = c^2
12^2 + 9^2 = c^2
144 + 81 = 225
15 = c
hypotenuse
sqrt (12^2 + 9^2)
sqrt ( 144 + 81)
sqrt (225)
= 15
To find the distance from stake Z to stake X, we can use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this problem, stake X and stake Y form one side of the right triangle, and stake Y and stake Z form the other side. We are given that the length of the string from stake X to stake Y is 12 yards and the length of the string from stake Y to stake Z is 9 yards.
Let's label the length of the string from stake Z to stake X as "d". Now we have the following equation:
d² = (12 yards)² + (9 yards)²
To solve for "d", we can square both sides of the equation:
d² = 12² + 9² = 144 + 81 = 225
Now we can take the square root of both sides to find the value of "d":
d = √225 = 15 yards
Therefore, the distance from stake Z to stake X is 15 yards.
So the correct answer is A. 15 yards.