Question

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The base and height of triangle are in ratio 2:3. Its area is 300 cm². Find the height and base

Answer 1

Answer:

Given :-

• Base and height of triangle are in ratio 2:3
• Area = 300 cm²

To Find :-

Height and base

Knowledge Required :—

Àrea of triangle = ½ × b × h unit²

• B is The Base
• H is the Height

Solution :-

As we know that

Area = ½ × Base × Height

Let the ratio be 2x and 3x.

300 = ½ × 2x × 3x

300 × 2 = 2x × 3x

600 = 2x × 3x

600 = 6x²

600/6 = x²

100 = x²

√(100) = x

√10 × 10 = x

10 = x

Hence :-

Sides are :- 2(10) = 20 cm and 3(10) = 30 cm

Verification :-

300 = ½ × 20 × 30

300 = 10 × 30

300 = 300

Hence, Verified.

Know More :-

Area of triangle = √[s(s-a)(s-b)(s-c]

Semiperimeter = Perimeter/2

Here,

S is the Semiperimeter

a,b and c are sides of triangle.

Answer 2

Given :

The base and height of triangle are in ratio 2:3. Its area is 300 cm².

To find :

• Height and base of the triangle

Solution :

• Area of trianlge = 300 cm²

Base and height of triangle are in ratio 2:3

Let the base be 2x and height be 3x

• As we know that

→ Area of triangle = 300cm²

→ ½ × base × height = 300

→ ½ × 2x × 3x = 300

→ 3x² = 300

→ x² = 300/3

→ x² = 100

→ x = √100

→ x = ±10 cm

Focus Zone : Length never be in negative

•°• Base of trianlge = 2x = 2*10 = 20 cm

•°• Height of trianlge = 3x = 3*10 = 30 cm

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