Question

the ratio of areas of two traingle is 2:3.the base of smaller angle is 6 cm.find the base of larger traingle.


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Answer 1

Given :-

The ratio of areas of two triangle = 2:3

The base of smaller angle = 6 cm

To Find :-

The base of larger triangle.

Analysis :-

Take the areas as variables 2x and 3x

Make an equation.

Find the value of x

Substitute their values and find the value of base.

Solution :-

We know that,

• b = Base
• h = Height
• a = Area

Given that,

The ratio of areas of two triangle = 2:3

The base of smaller angle = 6 cm

Let us consider the areas to be 2x and 3x.

According to the question,

$\sf 2x=\dfrac{1}{2} \times Base \times height$

$\sf \sf 2x=\dfrac{1}{2} \times 6 \times height$

Therefore,

$\sf x=\dfrac{3h}{2}$

$\sf 3x=\dfrac{1}{2} \times base \times height$

Putting value of x,

$\sf 3 \times \dfrac{3h}{2}=\dfrac{bh}{2}$

$\sf 3 \times 3=b$

$\sf =b=9$

Hence, the base of larger triangle is 9 cm