Question

The base and height of a triangle are in the ratio 3:2 and its area is 108 cm2 .find its base and height​

Answer 1

1/2 × b h = 108

=> b h= 108×2 = 216

=> 3x.2x= 216

=> 6x^2 = 216

=> x^2 = 216/6 = 36

X=6

Answer 2

Given :

• Base and height of triangle are in ratio 3:2.
• Area of Triangle = 108cm²

To Find :

• Base and Height of Triangle

Solution :

$\longmapsto\tt{Let\:Base\:be=3x}$

$\longmapsto\tt{Let\:height\:be=2x}$

$\longmapsto\tt{Area\:of\:Triangle=108{cm}^{2}}$

Using Formula :

$\boxed{Area\:of\:Triangle=\dfrac{1}{2}\times{base}\times{height}}$

Putting Values :

$\longmapsto\tt{108=\dfrac{1}{2}\times{3x}\times{2x}}$

$\longmapsto\tt{108\times{2}=6{x}^{2}}$

$\longmapsto\tt{\cancel\dfrac{216}{6}={x}^{2}}$

$\longmapsto\tt{\sqrt{36}={x}^{2}}$

$\longmapsto\tt\bold{x=6}$

So , The value of x is 6cm..

Therefore :

$\longmapsto\tt{Base=3(6)}$

$\longmapsto\tt\bold{18cm}$

$\longmapsto\tt{Height=2(6)}$

$\longmapsto\tt\bold{12cm}$

_______________________

VERIFICATION :

$\longmapsto\tt{108=\dfrac{1}{\cancel{2}}\times{\cancel{18}}\times{12}}$

$\longmapsto\tt{108=9\times{12}}$

$\longmapsto\tt\bold{108=108}$

HENCE VERIFIED