Question

The base of a Triangle is thrice its height. If the area of Triangle is 486cm², find the base and height of the triangle​

Answer 1

Answer:

Given :

• Base of Triangle is thrice its Height .
• Area of Triangle is 486 cm² .

To Find :

• Base and Height of the Triangle .

Solution :

$\longmapsto\tt{Let\:Height\:be=x}$

As Given that Base of Triangle is thrice its Height . So ,

$\longmapsto\tt{Base\:of\:Triangle=3x}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:\triangle=\dfrac{1}{2}\times{b}\times{h}}$

Putting Values :

$\longmapsto\tt{486=\dfrac{1}{2}\times{3x}\times{x}}$

$\longmapsto\tt{486\times{2}=3{x}^{2}}$

$\longmapsto\tt{972=3{x}^{2}}$

$\longmapsto\tt{\cancel\dfrac{972}{3}={x}^{2}}$

$\longmapsto\tt{\sqrt{324}=x}$

$\longmapsto\tt\bf{18=x}$

Value of x is 18 .

Therefore :

$\longmapsto\tt{Height\:of\:Triangle=x}$

$\longmapsto\tt\bf{18\:cm}$

$\longmapsto\tt{Base\:of\:Triangle=3(18)}$

$\longmapsto\tt\bf{54\:cm}$