Math, asked by singh987642, 8 months ago

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

Answered by gkhushboo630
30

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

Answered by BrainlyRaaz
52

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.

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