Question

A triangle has an area of 48 square centimeters. The height of the triangle is 6 centimeters. What is the base of the triangle?

Answer 1

Question :-

• A Triangle has an Area of 48 cm² . The Height of the Triangle is 6 cm . What is the Base of the Triangle ?

Answer :-

• Base of Triangle is 16 cm .

Explanation :-

As per the provided information in the given question, we have been given that the Area of Triangle is 48 cm² . It's Height is given as 6 cm . And, we have been asked to calculate the Base of Triangle .

For calculating the Base of Triangle , we will use the Formula :-

`\bigstar \: \: \: \boxed{ \sf{ \: Area \: _(Triangle) \: = \: (1)/(2) \: * \: B \: * \: H \: }}`

Where ,

• B denotes to the Base .
• H denotes to the Height .

Therefore , by Substituting the given values in the above Formula :-

`\dag \: \: \: \sf { Area \: _(Triangle) \: = \: (1)/(2) \: * \: Base \: * \: Height }`

`\longmapsto \: \: \: \sf {48 \: = \: \frac {1}{2} \: * \: Base \: * \: 6 }`

`\longmapsto \: \: \: \sf {48 \: * \: 2 \: = \: 1 \: * \: Base \: * \: 6}`

`\longmapsto \: \: \: \sf {96 \: = \: 1 \: * \: Base \: * \: 6}`

`\longmapsto \: \: \: \sf {96 \: = \: 6 \: * \: Base }`

`\longmapsto \: \: \: \sf {Base \: = \: \frac {96}{6} }`

`\longmapsto \: \: \: \textbf {\textsf {Base \: = \: 16 \: cm}}`

Hence :-

• Base of Triangle = 16 cm .

`\underline {\rule {180pt} {4pt}}`

Answer 2

Question : -

A triangle has an area of 48 square centimetres. The height of the triangle is 6 centimetres. What is the base of the triangle ?

Given : -

• Area of triangle = 48 cm²

• Height of triangle = 6 cm

To Find : -

• Base of triangle

Formula Used : -

`\blue{\boxed{Area \: of \: triangle = (1)/(2) * b * h}}`

Where ,

• b = Base of triangle

• h = Height of triangle

Concept : -

In this question the concept belongs to the areas of two dimensional shapes i.e. how we can find length , breadth or height with the help of given area .

So let's get started : -

`\longmapsto \: 48 = (1)/(2) * b * 6`

Now , transposing 2 to left hand side :

`\longmapsto \: 48 * 2 = 1 * b * 6`

Now , multiplying 48 with 2 and multiplying b with 1 and 6 :

`\longmapsto \: 96 = 6b`

Now , transposing 6 to left hand side :

`\longmapsto \: \cancel(96)/(6) = b`

Now , by cancelling them we get :

`\longmapsto \: \red{ \boxed{ \sf{b = 16 \: cm}}}`

• Therefore , base of triangle is of 16 cm

Verifying : -

We know that area of triangle is equal to 48 cm². So :

`\rightarrow \: (1)/( \cancel2) * \cancel{16} * 6 = 48`

Now , by cancelling 16 with 2 we get :

`\rightarrow \: 8 * 6 = 48`

So , by multiplying we get :

`\rightarrow \: 48 = 48`

That means :

`\rightarrow \: L.H.S = R.H.S`

• Hence , Verified .

Therefore, our answer is valid .

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