Question

The base and height of a triangle are in the ratio 2:3 and it's area is 216 cm spuare . Find the area of the triangle

Answer 1

Given,

Base:height = 2:3

Area of the triangle = 216 cm^2.......(1)

Assumptions,

Let the base of the triangle be 2x.....(2)

Let the height of the triangle be 3x...(3)

We know,

Area of the triangle = 1/2*b*h...........(4)

We have,

Area of the triangle = 216 cm^2

From (1) already given,

1/2*b*h = 216

From (4) we know,

1/2*2x*3x = 216

From (2) and (3) our assumptions,

Solving,

3*x^2 = 216

x^2 = 72

x = 6*root(2)

So, length = 2x = 12*root(2) cm

Breadth = 3x = 18*root(2) cm

Answer 2

Base:height = 2:3

Area of the triangle = 216 cm^2.......(1)

Assumptions,

Let the base of the triangle be 2x.....(2)

Let the height of the triangle be 3x...(3)

We know,

Area of the triangle = 1/2*b*h...........(4)

We have,

Area of the triangle = 216 cm^2

From (1) already given,

1/2*b*h = 216

From (4) we know,

1/2*2x*3x = 216

From (2) and (3) our assumptions,

Solving,

3*x^2 = 216

x^2 = 72

x = 6*root(2)

So, length = 2x = 12*root(2) cm

Breadth = 3x = 18*root(2) cm.

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Thanks!