Examples for Solve Length of side fire Triangle

Examples for Solve Length of side fire Triangle:

1) Solve the length of two side’s fire triangle is 29 cm and 30cm. If perimeter of the fire triangle is 81 cm, what is the length of third side of the fire triangle?

Solution:

Let third side length of the triangle is x cm then,

20 + 30 + x = 81

50+ x = 81

x = 81 -50

x = 31cm

Therefore length of third side of the fire triangle is 31cm.

How to find slope of a line?

Find the slope of the line where the points are ( 9,5) and (7,3) by using straight line tools.

Solution:

The formula for slope m = (y₁-y₂) / (x₁-x₂).

M = (5-3) / (9 -7).

M = 2 / 2.

= 1.

Thus the slope of line is 1.

General rules for multiplication

General rules for multiplication:

Positive x positive = positive

Negative x negative = positive

Positive x negative =negative

Negative x positive = negative

Positive x positive = positive:

Example:

x 4 =12

This two number are positive integers. So, answer is positive.

Negative x negative = positive

For example,

-4 x -3 = 12

This two number are negative integers .so, answer is positive.

Positive x negative =negative

For example,

4 x 3 =-12

One positive integer and one negative integer .so, answer is negative.

Negative x positive = negative

For example,

-4 x -3 =-12

One negative integer and one positive integer.so, answer is negative.

Solve the algebraic expression

Solve the algebraic expression:

4(x -1) + 2y - 5(x -y -4) + 5

Multiplying the integer terms

= 4x - 4 + 2y -5x + 5y + 20 + 5

Grouping the above terms

= -x + 7y + 21

Geometry Problem and Solution

Problem: Can two vertically opposite angles be supplement to each other? Draw a diagram to illustrate your answer


Let AB and CD bisect each other at right angles as shown in figure.







( Vertically opposite angles can be
supplements to each other)

Arithmetic Progressions

Arithmetic Progressions:
Consider the following lists of numbers :
(i) 1, 2, 3, 4, . . .
(ii) 100, 70, 40, 10, . . .
(iii) – 3, –2, –1, 0, . . .
(iv) 3, 3, 3, 3, . . .
(v) –1.0, –1.5, –2.0, –2.5, . . .
Each of the numbers in the list is called a term. In (i), each term is 1 more than the term preceding it. In (ii), each term is 30 less than the term preceding it. In (iii), each term is obtained by adding 1 to the term preceding it. In (iv), all the terms in the list are 3 , i.e., each term is obtained by adding (or subtracting) 0 to the term preceding it. In (v), each term is obtained by adding – 0.5 to (i.e., subtracting 0.5 from) the term preceding it. In all the lists above, we see that successive terms are obtained by adding a fixed number to the preceding terms. Such list of numbers is said to form an Arithmetic Progression ( AP ). So, an arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.

Slope of a Line

Slope of a Line:
A line in a coordinate plane forms two angles with the x-axis, which are supplementary.
The angle (say) θ made by the line l with positive direction of x-axis and measured anti clockwise
is called the inclination of the line. Obviously 0° ≤ θ ≤ 180° (below Fig ). We observe that lines parallel to x-axis, or coinciding with x-axis, have inclination of 0°. The inclination of a vertical line (parallel to coinciding with y-axis) is 90°.


Definition 1 If θ is the inclination of a line l, then tan θ is called the slope or gradient of the line l. The slope of a line whose inclination is 90° is not defined. The slope of a line is denoted by m. Thus, m = tan θ, θ ≠ 90° It may be observed that the slope of x-axis is zero and slope of y-axis is not defined.