Question

the base and height of a triangle are in the ratio 3:4 and its area is 96cm^2 . find its base and height

Answer 1

Given that the base and height of a triangle are in the ratio of 3:4.

Let the common ratio be x.

Then the height of the triangle = 4x.

And the base of the triangle = 3x.

Given that Area of triangle = 96cm^2.

We know that Area of triangle = 1/2 * b * h

96 = 1/2 * 3x * 4x

96 = 6x^2

x^2 = 96/6

x^2 = 16

x = 4cm.


Therefore the height of the triangle = 4x

                                                             = 4 * 4

                                                             = 16cm.



Therefore the base of the triangle = 3x

                                                          = 3 * 4

                                                           = 12cm.



Hope this helps!

Answer 2

Hey mate..
========

Let the base of a triangle be 3x cm

And the height of a triangle be 4x cm

Given,

Area of a triangle = 96 cm^2

We know,

Area of a triangle = $\frac{1}{2} \times base \times height$

$= > 96 = \frac{1}{2} \times 3x \times 4x$

$= > 96 = 6x {}^{2}$

$= > \frac{96}{6} = x {}^{2}$

$= > \sqrt{16 } = x$

Thus,

x = 4

So,

The base of the triangle

= (3 × 4) cm

= 12 cm

And, the height of the triangle

= ( 4 × 4 ) cm

= 16cm

Hope it helps !!