All High School Math Resources
Example Questions
Example Question #73 : Quadrilaterals
Erin is getting ready to plant her tulip garden. She wants to plant two tulips per square foot of garden. If her rectangular garden is enclosed by 24 feet of fencing, and the length of the fence is twice as long as its width, how many tulips will Erin plant?
16
64
48
32
24
64
We know that the following represents the formula for the perimeter of a rectangle:
In this particular case, we are told that the length of the fence is twice as long as the width. We can write this as the following expression:
Use this information to substitute in a variable for the length that matches the variable for width in our perimeter equation.
We also know that the length is two times the width; therefore, we can write the following:
The area of a rectangle is found by using this formula:
The area of the garden is 32 square feet. Erin will plant two tulips per square foot; thus, she will plant 64 tulips.
Example Question #1 : Squares
What is the length of a diagonal of a square with a side length ? Round to the nearest tenth.
A square is comprised of two 45-45-90 right triangles. The hypotenuse of a 45-45-90 right triangle follows the rule below, where is the length of the sides.
In this instance, is equal to 6.
Example Question #583 : High School Math
A square has sides of . What is the length of the diagonal of this square?
To find the diagonal of the square, we effectively cut the square into two triangles.
The pattern for the sides of a is .
Since two sides are equal to , this triangle will have sides of .
Therefore, the diagonal (the hypotenuse) will have a length of .
Example Question #584 : High School Math
A square has sides of . What is the length of the diagonal of this square?
To find the diagonal of the square, we effectively cut the square into two triangles.
The pattern for the sides of a is .
Since two sides are equal to , this triangle will have sides of .
Therefore, the diagonal (the hypotenuse) will have a length of .
Example Question #231 : Geometry
What is the length of the diagonal of a square with a side length of ?
To find the diagonal of a square, we must use the side length to create a 90 degree triangle with side lengths of , , and a hypotenuse which is equal to the diagonal.
Pythagorean’s Theorem states , where a and b are the legs and c is the hypotenuse.
Take and and plug them into the equation for and :
After squaring the numbers, add them together:
Once you have the sum, take the square root of both sides:
Simplify to find the answer: , or .
Example Question #1 : How To Find The Length Of The Diagonal Of A Square
What is the length of the diagonal of a 7-by-7 square? (Round to the nearest tenth.)
To find the diagonal of a square we must use the side lengths to create a 90 degree triangle with side lengths of 7 and a hypotenuse which is equal to the diagonal.
We can use the Pythagorean Theorem here to solve for the hypotenuse of a right triangle.
The Pythagorean Theorem states , where a and b are the sidelengths and c is the hypotenuse.
Plug the side lengths into the equation as and :
Square the numbers:
Add the terms on the left side of the equation together:
Take the square root of both sides:
Therefore the length of the diagonal is 9.9.
Example Question #1 : How To Find The Length Of The Diagonal Of A Square
The perimeter of a square is 48. What is the length of its diagonal?
Perimeter = side * 4
48 = side * 4
Side = 12
We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.
Therefore, we can use the Pythagorean Theorem to solve for the diagonal:
Example Question #1 : How To Find The Area Of A Square
ABCD and EFGH are squares such that the perimeter of ABCD is 3 times that of EFGH. If the area of EFGH is 25, what is the area of ABCD?
5
25
225
15
75
225
Assign variables such that
One side of ABCD = a
and One side of EFGH = e
Note that all sides are the same in a square. Since the perimeter is the sum of all sides, according to the question:
4a = 3 x 4e = 12e or a = 3e
From that area of EFGH is 25,
e x e = 25 so e = 5
Substitute a = 3e so a = 15
We aren’t done. Since we were asked for the area of ABCD, this is a x a = 225.
Example Question #2 : How To Find The Area Of A Square
A square has an area of 36. If all sides are doubled in value, what is the new area?
48
72
132
108
144
144
Let S be the original side length. S*S would represent the original area. Doubling the side length would give you 2S*2S, simplifying to 4*(S*S), giving a new area of 4x the original, or 144.
Example Question #1 : Squares
If the perimeter of a square is equal to twice its area, what is the length of one of its sides?
Area of a square in terms of each of its sides:
Area = S x S
Perimeter of a square:
Perimeter = 4S
So if 'the perimeter of a square is equal to twice its area':
2 x Area = Perimeter
2 x [S x S] = [4S]; divide by 2:
S x S = 2S; divide by S:
S = 2
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