Question

The base and the height of a triangle are in the ratio 3:2,if the area of the triangle is 48m²,find it's base and height.​

Answer 1

Step-by-step explanation:

Let the base and height be 3x and 2x,

As we know ,

Area of triangle = 1/2 × base × height

1/2 × 3x × 2x = 48

$3 {x}^{2} = 48$

${x}^{2} = 16$

$x = 4$

Now ,

Base = 3x = 12m

Height = 2x = 8m

Answer 2

Given :

• Base and Height of a Triangle are in the ratio 3:2 .
• Area of Triangle is 48 m² .

To Find :

• Base and Height of Triangle .

Solution :

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

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

Using Formula :

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

Putting Values : -

$\longmapsto\tt{48=\dfrac{1}{2}\times{3x}\times{2x}}$

$\longmapsto\tt{48\times{2}={6x}^{2}}$

$\longmapsto\tt{96={6x}^{2}}$

$\longmapsto\tt{\cancel\dfrac{96}{6}={x}^{2}}$

$\longmapsto\tt{\sqrt{16}=x}$

$\longmapsto\tt\bf{x=4}$

Value of x is 4 ..

Therefore :

$\longmapsto\tt{Base=3(4)}$

$\longmapsto\tt\bf{12\:m}$

$\longmapsto\tt{Height=2(4)}$

$\longmapsto\tt\bf{8\:m}$