Perimeter of a rectangle is equal to the perimeter of right angled triangle of height 12
Answers
Answer:
Here we will discuss about the area and perimeter of the triangle.
● If a, b, c are the sides of the triangle, then the perimeter of triangle = (a + b + c) units.
● Area of the triangle = √(s(s - a) (s - h) (s - c))
The semi-perimeter of the triangle, s = (a + b + c)/2
● In a triangle if 'b' is the base and h is the height of the triangle then
Area of triangle = 1/2 × base × height
Similarly,
area and perimeter of the triangle
1/2 × AC × BD 1/2 × BC × AD
Step-by-step explanation:
Area of right angled triangle
● If a represents the side of an equilateral triangle, then its area = (a²√3)/4
perimeter of an equilateral triangle
● Area of right angled triangle
A = 1/2 × BC × AB
= 1/2 × b × h
area of right angled triangle
Worked-out examples on area and perimeter of the triangle:
1. Find the area and height of an equilateral triangle of side 12 cm. (√3 = 1.73).
Solution:
Area of the triangle = √34 a² square units
= √34 × 12 × 12
= 36√3 cm²
= 36 × 1.732 cm²
= 62.28 cm²
Height of the triangle = √32 a units
= √32 × 12 cm
= 1.73 × 6 cm
= 10.38 cm
2. Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm.
Solution:
AB² = AC² - BC²
= 15² - 12²
= 225 - 144
= 81
Therefore, AB = 9
Therefore, area of the triangle = ¹/₂ × base × height
= ¹/₂ × 12 × 9
= 54 cm²
3. The base and height of the triangle are in the ratio 3 : 2. If the area of the triangle is 243 cm² find the base and height of the triangle.
Solution:
Let the common ratio be x
Then height of triangle = 2x
And the base of triangle = 3x
Area of triangle = 243 cm²
Area of triangle = 1/2 × b × h 243 = 1/2 × 3x × 2x
⇒ 3x² = 243
⇒ x² = 243/3
⇒ x = √81
⇒ x = √(9 × 9)
⇒ x = √9
Therefore, height of triangle = 2 × 9
= 18 cm
Base of triangle = 3x
= 3 × 9
= 27 cm
4. Find the area of a triangle whose sides are 41 cm, 28 cm, 15 cm. Also, find the length of the altitude corresponding to the largest side of the triangle.
Solution:
Semi-perimeter of the triangle = (a + b + c)/2
= (41 + 28 + 15)/2
= 84/2
= 42 cm
Therefore, area of the triangle = √(s(s - a) (s - b) (s - c))
= √(42 (42 - 41) (42 - 28) (42 - 15)) cm²
= √(42 × 1 × 27 × 14) cm²
= √(3 × 3 × 3 × 3 × 2 × 2 × 7 × 7) cm²
= 3 × 3 × 2 × 7 cm²
= 126 cm²
Now, area of triangle = 1/2 × b × h
Therefore, h = 2A/b
= (2 × 126)/41
= 252/41
= 6.1 cm