Question

The ratio of the areas of two triangles A1: A2 is
3:2. The corresponding bases are b1 and b2. The
heights of the triangles are equal. If b2 = 12 cm.
Find b1.​

Answer 1

Answer:

18cm

Step-by-step explanation:

For detailed solution view attachment.

Answer 2

The length of base of 1st triangle is 18cm.

The ratio of the areas of two triangles A₁ : A₂ is 3 : 2. The corresponding bases are b₁ and b₂ and heights of the triangles are equal.

We have to find the value of b₁ , if b₂ = 12 cm.

We know, the area of triangle = 1/2 × base × height

∴ the area of first triangle, A₁ = 1/2 × b₁ × h₁

And the area of 2nd triangle, A₂ = 1/2 × b₂ × h₂

A/C to question,

• A₁ : A₂ = 3 : 2
• h₁ = h₂ [ heights of triangles are equal ]
• b₂ = 12 cm

∴ A₁/A₂ = (1/2 × b₁ × h₁)/(1/2 × b₂ × h₂) = (b₁/b₂) × (h₁/h₂)

⇒ 3/2 = b₁/12 × 1/1

⇒ b₁ = 18 cm

Therefore the length of base of 1st triangle is 18cm.

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