HSPT Math : Concepts
Study concepts, example questions & explanations for HSPT Math
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Example Questions
Example Question #11 : How To Find The Perimeter Of A Rectangle
What is the perimeter of a rectangle with a width of 3 and a length of 10?
26
13
30
12
60
26
The formula for the perimeter of a rectangle is 
Plug in our given values to solve:
Example Question #1 : Isosceles Triangles
Two sides of an isosceles triangle are 20 and 30. What is the difference of the largest and the smallest possible perimeters?
10
0
30
15
The answer cannot be determined
10
The trick here is that we don't know which is the repeated side. Our possible triangles are therefore 20 + 20 + 30 = 70 or 30 + 30 + 20 = 80. The difference is therefore 80 – 70 or 10.
Example Question #1 : How To Find The Perimeter Of An Equilateral Triangle
A square rug border consists of a continuous pattern of equilateral triangles, with isosceles triangles as corners, one of which is shown above. If the length of each equilateral triangle side is 5 inches, and there are 40 triangles in total, what is the total perimeter of the rug?
The inner angles of the corner triangles is 30°.
124
188
208
180
200
188
There are 2 components to this problem. The first, and easier one, is recognizing how much of the perimeter the equilateral triangles take up—since there are 40 triangles in total, there must be 40 – 4 = 36 of these triangles. By observation, each contributes only 1 side to the overall perimeter, thus we can simply multiply 36(5) = 180" contribution.
The second component is the corner triangles—recognizing that the congruent sides are adjacent to the 5-inch equilateral triangles, and the congruent angles can be found by
180 = 30+2x → x = 75°
We can use ratios to find the unknown side:
75/5 = 30/y → 75y = 150 → y = 2''.
Since there are 4 corners to the square rug, 2(4) = 8'' contribution to the total perimeter. Adding the 2 components, we get 180+8 = 188 inch perimeter.
Example Question #1 : How To Find The Perimeter Of A Square
A circle with a radius 2 in is inscribed in a square. What is the perimeter of the square?
16 in
28 in
12 in
24 in
32 in
16 in
To inscribe means to draw inside a figure so as to touch in as many places as possible without overlapping. The circle is inside the square such that the diameter of the circle is the same as the side of the square, so the side is actually 4 in. The perimeter of the square = 4s = 4 * 4 = 16 in.
Example Question #2 : How To Find The Perimeter Of A Square
Square X has 3 times the area of Square Y. If the perimeter of Square Y is 24 ft, what is the area of Square X, in sq ft?
72
54
112
144
108
108
Find the area of Square Y, then calculate the area of Square X.
If the perimeter of Square Y is 24, then each side is 24/4, or 6.
A = 6 * 6 = 36 sq ft, for Square Y
If Square X has 3 times the area, then 3 * 36 = 108 sq ft.
Example Question #291 : Plane Geometry
A square has an area of 
The area of the given square is given by 
Example Question #1 : Rectangles
A rectangle has a width of 2x. If the length is five more than 150% of the width, what is the perimeter of the rectangle?
10(x + 1)
6x2 + 5
5x + 10
6x2 + 10x
5x + 5
10(x + 1)
Given that w = 2x and l = 1.5w + 5, a substitution will show that l = 1.5(2x) + 5 = 3x + 5.
P = 2w + 2l = 2(2x) + 2(3x + 5) = 4x + 6x + 10 = 10x + 10 = 10(x + 1)
Example Question #2 : Quadrilaterals
ABCD is a parallelogram. BD = 5. The angles of triangle ABD are all equal. What is the perimeter of the parallelogram?
If all of the angles in triangle ABD are equal and line BD divides the parallelogram, then all angles in triangle BDC must be equal as well.
We now have two equilateral triangles, so all sides of the triangles will be equal.
All sides therefore equal 5.
5+5+5+5 = 20
Example Question #1311 : Concepts
A square has a length of 
The square perimeter is 
Substitute and multiply to find the perimeter.
There are 
Multiply the perimeter with 
Example Question #131 : Quadrilaterals
Give the perimeter of the above rectangle in centimeters, using the conversion factor 
The perimeter of the rectangle is 
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