Question

Base and height of triangle are in ratio 2:3 and its area is 108 square cm . Find base and height

Answer 1

Answer:

Base= 12cm

Height= 18cm

Step-by-step explanation:

Let, base be 2x and height be 3x

Now,

$area \: of \: triangle = 108 {cm}^{2} \: \: \: \: (given) \\ = > \frac{1}{2} \times \: base \: \times \: height = 108 {cm}^{2} \\ = > \frac{1}{2} \times 2x \times 3x = 108 {cm}^{2} \\ = > 3 {x}^{2} = 108 {cm}^{2} \\ = > {x}^{2} = \frac{108 {cm}^{2} }{3} \\ = > {x}^{2} = 36 {cm}^{2} \\ = > x = \sqrt{36 {cm}^{2} } \\ = > x = 6cm$

Therefore,

Base=

$2x \\ = 2 \times 6cm \\ = 12cm$

and,

Height=

$3x \\ = 3 \times 6x \\ = 18cm$