Scalene triangle is a triangle with all sides of different lengths.
All angles are different, too.
So, no sides are equal and no angles are equal.
Formula for Area of Scalene Triangle :
= √[s(s - a)(s - b)(s - c)]
where
s = (a + b + c)/2
Here a, b and c are side lengths of the triangle.
Example 1 :
Find the area of the scalene triangle whose length of sides are 12 cm, 18 cm and 20 cm.
Solution :
Because the lengths of the three sides are different, the triangle is scalene triangle.
s = (a + b + c)/2
Substitute 12 for a, 18 for b and 20 for c.
= (12 + 18 + 20)/2
= 50/2
= 25
Formula for area of scalene triangle :
= √[s(s - a)(s - b)(s - c)]
Substitute.
= √[25(25 - 12)(25 - 18)(25 - 20)]
= √(25 x 13 x 7 x 5)
= 5√455 cm^{2}
Example 2 :
The sides of a scalene triangle are 12 cm, 16 cm and 20 cm. Find the altitude to the longest side.
Solution :
In order to find the altitude to the longest side of a triangle, first we have to find the area of the triangle.
s = (a + b + c)/2
Substitute 12 for a, 16 for b and 20 for c.
s = (12 + 16 + 20)/2
= 48/2
= 24
Formula for area of scalene triangle :
= √[s(s - a)(s - b)(s - c)]
Substitute.
= √[24 x (24 - 12) x (24 - 16) x (24 - 20)]
= √(24 x 12 x 8 x 4)
= 96 cm^{2}
Because we want to find the altitude to the longest side, the longest side will be the base of the triangle as shown below.
Here, the longest side is 20 cm.
Area of the above triangle = 96 cm^{2}
1/2 x 20 x h = 96
10h = 96
Divide each side by 10.
h = 9.6
So, the altitude to the longest side is 9.6 cm.
Example 3 :
The sides of a scalene triangle are in the ratio (1/2) : (1/3) : (1/4). If the perimeter is 52 cm, then find the length of the smallest side.
Solution :
From the given information, the sides the triangle are
x/2, x/3 and x/4
Perimeter of the triangle = 52 cm
x/2 + x/3 + x/4 = 52
(6x + 4x + 3x)/12 = 52
13x/12 = 52
13x = 624
x = 48
Lengths of the sides :
x/2 = 24
x/3 = 16
x/4 = 12
So, the length of smallest side is 12 cm.
Example 4 :
The area of the scalene triangle is 216 cm^{2} and the sides are in the ratio 3 : 4 : 5. Find the perimeter of the triangle.
Solution :
From the given information, the sides the triangle are
3x, 4x and 5x
s = (3x + 4x + 5x)/2
s = 6x
Area of the triangle = 216 cm^{2}
√[s(s - a)(s - b)(s - c)] = 216
√[6(6x - 3x)(6x - 4x)(6x - 5x)] = 216
√[6(3x)(2x(x] = 216
√(36x^{4}) = 216
6x^{2} = 216
x^{2} = 36
x = 6
Lengths of the sides :
3x = 18
4x = 24
5x = 30
Perimeter of the given scalene triangle is
= 18 + 24 + 30
= 72 cm
Example 5 :
One side of a right angle scalene triangle is twice the other, and the hypotenuse is 10 cm. Find the area of the triangle.
Solution :
Let 'x' be the length of one of the legs of the triangle.
Then, the length of the other leg is 2x.
Using Pythagorean theorem,
x^{2} + (2x)^{2 }= 10^{2}
x^{2} + 4x^{2 }= 100
5x^{2 }= 100
x^{2}^{ }= 20
√x^{2}^{ }= √20
x = √(4 x 5)
x = 2√5
Then,
2x = 2(2√5)
= 4√5
Area of the given right scalene triangle is
= (1/2)(x)(2x)
= (1/2)(2√5)(4√5)
= 20 cm^{2}
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and Venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
©All rights reserved. onlinemath4all.com
May 19, 22 12:17 PM
Circles Worksheet
May 19, 22 12:14 PM
SAT Math Practice Worksheets - Topic wise worksheet with step by step explanation for each question
May 19, 22 12:10 PM
SAT Math Practice - Different Topics - Concept - Formulas - Example problems with step by step explanation