Question

The baseand height of the triangle are in the ratio3:2 and its area is108 sq.cm. Find its base and height

Answer 1

SOLUTION :

The base and the height of a triangle = 3:2 respectively     (given)

The area of the triangle = 108 cm sq.        (given)

To be found :-

The base and height of the triangle

Let,

Base of the triangle be 3x cm

and height of the triangle be 2x cm

We know that,

Area of triangle = $\bf{ \frac{1}{2} } \times b\times h$ unit sq.

[ ∴ In which b is the base and h is the height of the triangle ]

⇒$\bf{108}$ =  $\bf{ \frac{1}{2} } \times 3x \times 2x$

⇒ $\bf{108}$ =  $\bf{ {3x}^{2} }$

⇒ $\bf{ \frac{108}{3} }$ =  $\bf{ {x}^{2} }$

⇒ $\bf{36}$=  $\bf{ {x}^{2} }$

⇒ $\bf{ \sqrt{36} }$ = $\bf{x}$

⇒ $\bf{6 = x}$

∴ Value of x = 6

So,

Base of the triangle = 3x cm = 3 × 6 = 18 cm

and height of the triangle = 2x cm = 2 × 6 = 12 cm

Hence,

The base of the triangle is 18 cm

And the height of the triangle is 12 cm