All GED Math Resources
Example Questions
Example Question #14 : Pythagorean Theorem
Determine the hypotenuse of a right triangle if the side legs are respectively.
Write the Pythagorean Theorem to find the hypotenuse.
Substitute the dimensions.
Square root both sides.
The answer is:
Example Question #15 : Pythagorean Theorem
A car left City A and drove straight east for miles then it drove straight north for miles, where it stopped. In miles, what is the shortest distance between the car and City A?
Start by drawing out what the car did.
You'll notice that a right triangle will be created as shown by the figure above. Thus, the shortest distance between the car and City A is also the hypotenuse of the triangle. Use the Pythagorean Theorem to find the distance between the car and City A.
Example Question #16 : Pythagorean Theorem
You want to build a garden in the shape of a right triangle. If the two arms will be 6ft and 8ft, what does the length of the hypotenuse need to be?
You want to build a garden in the shape of a right triangle. If the two arms will be 6ft and 8ft, what does the length of the hypotenuse need to be?
To find the length of a hypotenuse of a right triangle, simply use the Pythagorean Theorem.
Where a and b are the arm lengths, and c is the hypotenuse.
Plug in our knowns and solve.
Note that we could also have found c by identifying a Pythagorean Triple:
3x-4x-5x
3(2)-4(2)-5(2)
6-8-10
Example Question #17 : Pythagorean Theorem
Note: Figure NOT drawn to scale.
Refer to the above diagram.
Which is true of ?
By the Pythagorean Theorem, if and are the lengths of the shorter two sides, or legs, of a right triangle, and is the length of the longest side, or hypotenuse, of the triangle, then
Set :
Since we are trying to determine between which two of the consecutive integers in the set falls, it suffices to find out between which two of their squares falls. Each square is the product of the integer and itself, so:
,
or, substituting,
It follows that
.
Example Question #18 : Pythagorean Theorem
You are visiting a friend who has right-triangular shaped pool. You are seeing who can swim around the perimeter of the pool fastest. If the long side is 20 meters, and second shortest side is 15 meters long, how long is the shortest side?
You are visiting a friend who has right-triangular shaped pool. You are seeing who can swim around the perimeter of the pool fastest. If the long side is 20 meters, and second shortest side is 15 meters long, how long is the shortest side?
Let's begin by recalling Pythagorean Theorem
So, we know that c is our hypotenuse or longest side.
a and b are our shorter sides. It doesn't really matter which one is which.
Let's plug in and solve!
So, our answer is
Example Question #21 : Pythagorean Theorem
Find the area of rectangle in the figure below.
The area of the rectangle cannot be found with the given information.
Notice that the hypotenuse of the right triangle is also the length of the rectangle.
Start by using Pythagorean's Theorem to find the length of .
Next, recall how to find the area of a rectangle:
Example Question #21 : Pythagorean Theorem
A right triangle has hypotenuse with length 20 and a leg of length 9. The length of the other leg is:
Between 16 and 17.
Between 15 and 16.
Between 18 and 19.
Between 17 and 18.
Between 17 and 18.
By the Pythagorean Theorem, if we let be the length of the hypotenuse, or longest side, of a right triangle, and and be the lengths of the legs, the relation is
Set and , and solve for :
Square the numbers - that is, multiply them by themselves:
Subtract 81 from both sides to isolate :
To find out what integers falls between, it is necessary to find the perfect square integers that flank 319. We can see by trial and error that
,
so
The length of the second leg thus falls between 17 and 18.
Example Question #22 : Pythagorean Theorem
You recently bough a book end whose face forms a right triangle. You want to know the length of the longest side, but you don't have a ruler. Luckily, you know that the two shorter sides are 18 inches and 24 inches. Find the length of the last side.
You recently bough a book end whose face forms a right triangle. You want to know the length of the longest side, but you don't have a ruler. Luckily, you know that the two shorter sides are 18 inches and 24 inches. Find the length of the last side.
The problem describes a right triangle with two known sides. Finding the last side sounds like a job for Pythagorean Theorem. If you look carefully, you might see another way.
So, recall the classic:
We know a and b, and we need to find c.
So our answer is 30.
The alternate way to solve this is to see that we have a 3/4/5 Pythagorean Triple.
This means that our side lengths follow the ratio 3:4:5
We can see this by dividing our two given sides by 6.
So our scale factor is 6. This means we can get our answer by multiplying 5 and 6
So we get the same thing. Keep an eye out for Pythagorean Triples when working with right triangles in order to solve problems faster!
Example Question #23 : Pythagorean Theorem
Find the perimeter of an isosceles trapezoid that has an upper base of , an altitude to the base of , and diagonals of .
Start by drawing out the trapezoid in question.
Notice that triangle is a right triangle. Thus, we can use the Pythagorean theorem to find the length of segment .
Since we know that is also , then that means the length of segment must also be .
Now, we can use the Pythagorean Theorem again to find the length of .
Now we can find the perimeter of the entire isosceles trapezoid.
Make sure to round to two places after the decimal.
Example Question #23 : Pythagorean Theorem
A rectangle and circle share the same center as shown by the figure below.
Find the area of the circle.
The area of the circle cannot be determined.
Notice that the diagonal of the rectangle is also the diameter of the circle. We can use the Pythagorean Theorem to find the length of the diagonal.
From this, we can find the radius of the circle.
Recall how to find the area of a circle.
Plug in the given radius.