Question

The base and height of a triangle are in the ratio of 3:5 . If area is 120 cm^2,find its base and height

Answer 1

Answer:

if the base is 3x cm then height is 5xcm

1/2.3x.5x=120

15x^2=240

x^2=16

x=4

base =3.4cm=12cm

height zijn=5.4cm=20cm

Answer 2

Given :-

Ratio of the base and height = 3:5

Area of the triangle = 120 cm²

To Find :-

The base of the triangle.

The height of the triangle.

Analysis :-

Take the base and height of the triangle as 3x and 5x

Make an equation and solve to get the value of x

Substitute the value of x in 3x and 5x in order to get the value of base and height.

Solution :-

We know that,

• b = Base
• h = Height
• a = Area

Given that,

Ratio of base and height = 3:5

Area = 120 cm²

We know, the area of the triangle =  ½ (b × h)

Let us make an equation by taking variable x

$\longrightarrow \sf \dfrac{1}{2} (3x \times 5x)=120 \: cm^{2}$

$\longrightarrow \sf 3x \times 5x=\dfrac{120}{2}$

$\implies \sf x=\sqrt{\dfrac{60}{15} }$

$\implies \sf x=4$

Substituting the values of 3x and 5x

$\sf 3x \implies 3 \times 4=12 \: cm$

$\sf 5x \implies 5 \times 4=20 \: cm$

Base = 12 cm

Height = 20 cm

Therefore, the base is 12 cm and height is 20 cm

To Note :-

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.

Area of a Triangle = A = ½ (b × h) square units