Question

The ratio the areas of two triangles with equal

height is 3:2. The base of the larger triangle is 18cm.

Find the corresponding base of the smaller triangle.​

Answer 1

Answer:

12cm

Step-by-step explanation:

Given,

Heights of two triangles are equal .

Ratio of the areas of the triangle = 3 : 2

Base of the larger triangle = 18cm

To Find :-

Corresponding height of the smaller triangle

How To Do :-

As they given the ratio of the area of the triangles we need to equate that ratio of the formula of area of the triangle. After equating as there both heights are same we can cancel that and we need to find the base of the smaller triangle by doing cross multiplication of the ratios.

Formula Required :-

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

→ A = 1/2 × b × h

Solution :-

Let ,

The bigger triangle be :- Δ₁

The smaller triangle be :- Δ₂

$\implies \triangle_1=\dfrac{1}{2}\times b_1\times h_1$

$\triangle_2=\dfrac{1}{2}\times b_2\times h_2$

∴ h₁ = h₂

b₁ = 18cm

According to Question :-

$\dfrac{\triangle_1}{\triangle_2}=\dfrac{3}{2}$

$\dfrac{\dfrac{1}{2}\times b_1\times h_1}{\dfrac{1}{2}\times b_2\times h_2}=\dfrac{3}{2}$

$\dfrac{b_1\times h_1}{b_2\times h_2}=\dfrac{3}{2}$

Substituting the values :-

$\dfrac{18cm\times h_2}{b_2\times h_2}=\dfrac{3}{2}$

$\dfrac{18cm}{b_2}=\dfrac{3}{2}$

18cm × 2 = 3 × b₂

36cm = 3b₂

b₂ = 36cm/3

b₂ = 12cm

∴ Corresponding base of the small triangle = 12cm