Problem 1 :
Two sides of a triangle are 7 and 13 centimeters. The perimeter of is 27 cm. Find the third side.
Solution :
Let a, b and c be the sides of the triangle.
a = 7, b = 13
Perimeter = Sum of all the sides
a + b + c = 27
7 + 13 + c = 27
20 + c = 27
c = 27 - 20
c = 7 cm
Problem 2 :
Find the area of the triangle given below.
Solution :
Base = 8 and height = 4
Area of the triangle = (1/2) x base x height
= (1/2) x 8 x 4
= 16 cm^{2}
Problem 3 :
If a square has an area of 49 ft^{2}, what is the length of one of its sides? The perimeter ?
Solution :
Area of the square = 49 ft^{2}
a^{2} = 49
a^{2} = 7^{2}
a = 7
Length of one sides of the triangle is 7 cm.
Perimeter = 4a
= 4 (7)
= 28 cm
Problem 4 :
If a rectangle has a width of 4, how long must its length be so that the area is 36 ?
Solution :
Width of the rectangle = 4
Let l be the length of the rectangle.
Area of the rectangle = length x width
36 = 4 x l
l = 36/4
l = 9
Problem 5 :
If one angle of a right triangle is 70 degree. What are the other 2 angles ?
Solution :
Since it is a right triangle, one of the angle should be 90 degree. Let x be the third angle measure.
Sum of interior angles of the triangle = 180
70 + 90 + x = 180
160 + x = 180
x = 180 - 160
x = 20
Problem 6 :
Find b.
Solution :
Since it is right triangle, it holds the Pythagorean theorem.
5^{2} = 4^{2} + b^{2}
25 = 16 + b^{2}
25 - 16 = b^{2}
b^{2 }= 9
b = 3
Problem 7 :
What is the diameter of the circle with an area of 16π ?
Solution :
Area of the circle = 16π
πr^{2} = 16π
r^{2} = 16
r = 4
d = 2(radius)
d = 2(4)
d = 8
So, the diameter of the circle is 8.
Problem 8 :
What is the circumference of the circle having an area of 25π (allow π = 3.14)
Solution :
Area of the circle = 25π
πr^{2} = 25π
r^{2} = 25
r = 5
Circumference of the circle = πd
= π(10)
= 20π
Problem 9 :
If the box has a height of 4 in, a length of 12 in and volume of 240 in^{3}, what is the box's width.
Solution :
Height of the box = 4 inches, length = 12 inches
Let w be the width if the box.
Volume of the box = 240 in^{3}
Volume of cuboid = length x width x height
4 x w x 12 = 240
w = 240/(4 x 12)
w = 5 inches
Problem 10 :
Find the volume of cylinder whose radius and height are 2 and 7 respectively.
Solution :
Volume of cylinder = πr^{2}h
Radius = 2 and height = 7
Volume = (22/7) x 2^{2} x 7
= 88
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