Download Applications of the System of Linear Equations

Module 3
Geometric Problems
Applications of the System of
Linear Equations
Objectives
At the end of this period I should be able to:
1. recall concepts of the system of linear
equations;
2. solve word problems involving system
of linear equations particularly geometric
problems;
3. participate actively in class
discussions.
In a Nut Shell
What to remember for Geometric problems
(perimeter of a rectangle)
∗ 𝑊𝑒 ℎ𝑎𝑣𝑒 𝑡𝑜 𝑘𝑛𝑜𝑤 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡 𝑓𝑜𝑟𝑚𝑢𝑙𝑎𝑠
𝑖𝑛𝑣𝑜𝑙𝑣𝑒𝑑 𝑖𝑛 𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑦.
𝑃 = 2𝑙 + 2𝑤
P is the perimeter
𝑙 is the length
w is the width
Let’s Put On Our Thinking Hats
1. Two angles are complementary.
The larger angle is 9 less than
twice the smaller angle. Find the
two angles.
Adapted from: Exploring Mathematics, REX; Intermediate Algebra, MSA; Intermediate Algebra, Phoenix; Intermediate Algebra, Salesiana
In a Nut Shell
What to remember for Geometric problems
Complementary Angles
𝐴𝑛𝑔𝑙𝑒 𝑃𝑎𝑖𝑟𝑠
𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 90°
Let’s Put On Our Thinking Hats
2. A square and an equilateral
triangle have the same
perimeter. The sum of one side
of the square and one side of the
triangle is 28cm. Find the length
of one side of each figure.
Adapted from: Exploring Mathematics, REX; Intermediate Algebra, MSA; Intermediate Algebra, Phoenix; Intermediate Algebra, Salesiana
In a Nut Shell
What to remember for Geometric problems
Equilateral Triangle
a triangle in which all
three sides are equal
Let’s Put On Our Thinking Hats
3. The perimeter of an isosceles
triangle is 38 cm. The total
length of the two equal legs is 6
more than thrice the length of
the base. Find the lengths of the
three sides.
Adapted from: Exploring Mathematics, REX; Intermediate Algebra, MSA; Intermediate Algebra, Phoenix; Intermediate Algebra, Salesiana
In a Nut Shell
What to remember for Geometric problems
Isosceles Triangle
a triangle in which
two sides are equal
in length
Let’s Put On Our Thinking Hats
4. The perimeter of a square Q is
the same numerical value as the
side x of the rectangle P. The
perimeter of the rectangle is 84.
Find the x and y.
3y
P
x
Q
y
Adapted from: Exploring Mathematics, REX; Intermediate Algebra, MSA; Intermediate Algebra, Phoenix; Intermediate Algebra, Salesiana
In a Nut Shell
What to remember for Geometric problems
Perimeter of a Square
𝑃 = 4𝑠
P is the perimeter
𝑠 is the side
Let’s Put On Our Thinking Hats
5. Two angles are supplementary.
If the larger angle is twice the
smaller, what are the measures of
the two angles?
Adapted from: Exploring Mathematics, REX; Intermediate Algebra, MSA; Intermediate Algebra, Phoenix; Intermediate Algebra, Salesiana
In a Nut Shell
What to remember for Geometric problems
Supplementary Angles
𝐴𝑛𝑔𝑙𝑒 𝑃𝑎𝑖𝑟𝑠
𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 180°