The base and height of triangles are in the ratio 2:3 .if the area of the triangle is 108 cm square ,find its base and height
Answers
Step-by-step explanation:
Let ratio be 2x,3x respectively .
Formula ofArea of Triangle = 1/2× Base × Height
Area = 108cm² (given)
108cm²=1/2×2x×3x
108cm² × 2= 6x²
216cm² = 6x²
216/6 cm =x²
36 cm = x²
x=6 cm
Base=2x=12cm
Height =3x=18cm
Given :
- The base and height of triangles are in the ratio 2:3 .
- The area of the triangle is 108 cm square.
To find :
- Its base and height =?
Step-by-step explanation :
The area of the triangle is 108 cm square. [Given]
Let, the base of the triangle be 2x.
Then, the height of the triangle be 3x.
We know that,
Area of triangle = 1/2 × base × height
Substituting the values in the above formula, we get,
➮ 108 = 1/2 × 2x × 3x
➮ 108 = 1/2 × 6x²
➮ 6x² = 108 × 2
➮ 6x² = 216
➮ x² = 216/6
➮ x² = 36
____
➮ x = √6 × 6
➮ x = 6
Therefore, We get the value of x = 6.
Hence,
The base of the triangle, 2x = 2 × 6 = 12 cm
Then, the height of the triangle be 3x = 3 × 6 = 18 cm
Verification :
It is Given that :
Area of triangle = 108 cm².
The base of the triangle = 12 cm.
Then, the height of the triangle = 18 cm.
We know that,
Area of the triangle = 1 / 2 × base × height
Substituting the values in the above formula, we get,
108 = 1/2 = 12 × 18
108 = 6 × 18
108 = 108
LHS = RHS
Hence, it is verified.