Question

Ratio of areas of two triangle with equal heights is 2:3. If base of the smaller triangle is 4 cm, then what is the corresponding base of the bigger triangle?​

Answer 1

Answer :

• Corresponding base of the bigger triangle (i.e, the triangle with area A₁), b₂ = 6 cm

Explanation :

Given :

• Ratio of the areas of the two triangle, A₁ : A₂ = 2 : 3
• Base of the smaller triangle (i.e, the triangle with area A₁), b₁ = 4 cm
• Height of the triangle are equal.

To find :

• Corresponding base of the bigger triangle (i.e, the triangle with area A₁), b₂ = ?

Knowledge required :

• Formula for Area of a triangle :

⠀⠀⠀⠀⠀⠀⠀⠀⠀A = ½ × b × h⠀

[Where : A,b and h are the area, base and height of the triangle, respectively]

Solution :

Let the height of the two triangles be h cm (Since, they are equal).

[The ratio of the areas of the triangle will be equal to the ratio of the area of the triangle (in form of formula)]

Now, by using the formula for area of a triangle, we get :

⠀⠀⠀=> A₁/A₂ = (½ × b₁ × h)/(½ × b₂ × h)

⠀⠀⠀=> ⅔ = (½ × 4 × h)/(½ × b₂ × h)

⠀⠀⠀=> ⅔ = 4/b₂

⠀⠀⠀=> 2 × b₂ = 4 × 3

⠀⠀⠀=> 2b₂ = 12

⠀⠀⠀=> b₂ = 12/2

⠀⠀⠀=> b₂ = 6

⠀⠀⠀⠀⠀⠀∴ b₂ = 6 cm

Hence, the corresponding base of the bigger triangle (i.e, the triangle with area A₁) is 6 cm.

Answer 2

Question:-

• Ratio of areas of two triangle with equal heights is 2:3. If base of the smaller triangle is 4 cm, then what is the corresponding base of the bigger triangle?

Given:-

• Ratio of areas of two triangle with equal heights is 2:3.
• base of the smaller triangle is 4 cm.

To Find:-

• corresponding base of the bigger triangle = ?

Formula Used:-

$\star{\boxed{\sf{formula \: of \: triangle = \frac{1}{2} \times b \times h}}}$

Solution:-

$\sf \: = \frac{area \: of \: smaller \: triangle}{area \: of \: bigger \: triangle} = \frac{2}{3}$

$\implies \: \sf\frac{ \frac{1}{2} \times height \: of \: smaller \: triangle \times \: base \: of \: smaller \: triangle }{ \frac{1}{2} \times \: height \: of \: bigger \: triangle \times \: base \: of \: smaller \: triangle } = \frac{2}{3}$

$\sf \: = \frac{3}{2} \times 4$

$\purple{\boxed{ \implies 6 \: cm}}$

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