Question

height of a triangle are in ratio 3:2 and its area is 108 sq cm find the base and height​

Answer 1

Given : Area of A triangle are in the ratio 3:2 and its area is 108 cm² .

To Find : Find the Base and Height

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SolutioN :

☆ Formula Used :

• Area(Triangle) = 1/2 × Base × Height

☆ Let the Ratios :

• ➟ Base = 3y
• ➟ Height = 2y

☆ Calculating the Value of y :

$➺ \qquad$ Area = 1/2 × Base × Height

$\\ ➺ \qquad$ 108 = 1/2 × 2y × 3y

$\\ ➺ \qquad$ 108 = 1/2 × 6y

• Cancelling 2 with 6y :

$\\ ➺ \qquad$ 108 = 1 × 3y

$\\ ➺ \qquad$ 108 = 3y

$\\ ➺ \qquad$ 108/3 = y

• Cancelling 108 with 3 :

$\\ ➺ \qquad \; {\underline{\boxed{\pmb{\red{\frak{ y = 36 }}}}}} \; {\green{\bigstar}}$

☆ Calculating the Base and Height :

• Base = 3y = 3(36) = 108 cm
• Height = 2y = 2(36) = 72 cm

$\therefore \;$ Base of the Triangle is 108 cm and the Height is 72 cm .

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Answer 2

Answer:

Hence, base = 18cm and height = 12cm

Step-by-step explanation:

Given the ratio of base and height is 3:2 and area is 108sq cm.

We have to find the height and base of a triangle.

Let base = 3x

height = 2x

Area of a triangle =  1/2 × base × height

108 =1/2 × 3x × 2x

108 = 3x²

x² = 108/3 = 36

x = 6cm

Therefore, base = 3x = 3(6) = 18cm

Height = 2x = 2(6) = 12cm.