Question

A square and a triangle have equal area.The ratio of side of the square and the height of the triangle is 2 : 3. Find the ratio of the base and the height.
Solve it soon i am getting a wrong answer.​

Answer 1

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The ratio of side of the square and the height of the triangle is 2 : 3

Let the side of the square be 2x and height of the triangle be 3x

area of square = area of triangle

(side)^2 = 1/2×b×h

(2x)^2 = 1/2 × b × 3x

4x^2 = 3x/2 × b

4x^2 × 2/3x = b

6x^2/3x = b

=> b = 6 × x × x/3 × x

=> b = 2x

the ratio of the base and the height

= 2x/3x

= 2/3

= 2:3

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Answer 2

Solution :-

Given : A square and a triangle have equal area. The ratio of side of the square and the height of the triangle is 2 : 3.

Let the side of the square and the height of the triangle be 2x and 3x respectively.

According to the question,

Area of square = Area of rectangle

=> (side)² = ½ × b × h

=> (2x)² = ½ × b × 3x

=> 4x² = 3x/2 × b

=> b = (4x² × 2)/3x = 8x/3

Ratio of the base and the height = Base/Height

= (8x/3)/(3x)

= (8)/(3 × 3)

= 8/9

Hence,

Ratio of the base and the height = 8 : 9