Question

in a triangle the height is double the base and area is 400cm find the length of base and height​

Answer 1

Given -

• Area of triangle is 400 cm

• Height is double the base

To Find -

• Length of height and base

Formula used -

• Area of triangle

Solution -

In the question, we are given with the area of the Triangle, and a statement is given that the height is double of the base, and we need to find the length of base and height. For that, we will give a name to height and base, then we will apply the formula of area of triangle, then we will solve the question further. Let's do it!

Let -

The base be considered as x

Height be considered as 2x

So -

Area = 400 cm

Height = 2x cm

Base = x cm

Area of triangle -

$\sf \frac{1}{2} \: \times \: b \: \times \: h$

On substituting the values -

$\sf \longrightarrow \: 400 \: = \: \dfrac{1}{2} \: \times \: x \: \times \: 2x$

$\sf \longrightarrow \: 400 \: = \dfrac{1}{ \cancel{2}} \: \times \: x \: \cancel{2}x$

$\sf \longrightarrow \: 400 \: = {x}^{2}$

$\sf \longrightarrow \: \sqrt{400} \: = x$

$\sf \longrightarrow \: 20 \: = x$

Now -

We will multiple the obtained value with 20 to find the value of height.

$\sf \longrightarrow \: b \: = 20 \: cm$

$\sf \longrightarrow \: h \: = 20 \: \times \: 2 \: = 40 \: cm$

Verification -

$\sf \longrightarrow \: a \: = \dfrac{1}{2} \: \times \: b \: \times \: h$

$\sf \longrightarrow \: 400 \: cm \: = \frac{1}{2} \: \times 20 \: \times \: 40 \: \: cm$

$\sf \longrightarrow \: 400 \: = \dfrac{1}{ \cancel{2}} \: \times \: \cancel{20} \: \times \: 40 \: \: cm$

$\sf \longrightarrow \: 400 \: cm \: = 400 \: cm$

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Answer 2

${\large{\pmb{\sf{\underline{RequirEd \; Solution...}}}}}$

Understanding the question: This question says that we have to find out the length of base and the height of the triangle whose area is given as 400 centimetres and it's height is double the base. Symbol to show triangle is △. Let us solve this question properly!

Given that:

⋆ Height is double the base in that △

⋆ Area of that △ is 400 centimetres

To find:

⋆ The length of base of the △

⋆ The height of the △

Solution:

⋆ The length of base of the △ is 20 cm

⋆ The height of the △ is 40 cm

Assumptions:

⋆ Let us assume the base as a

⋆ Let us assume the height as 2a (as the height is double than the base)

Using concept:

⋆ Formula to find out the area of the triangle.

Using formula:

${\small{\underline{\boxed{\sf{Area \: of \: \triangle \: = \dfrac{1}{2} \times Base \times Height}}}}}$

Full Solution:

~ Firstly by using the formula to find area of triangle let us find out the length of the base. Let's do it!

${\small{\underline{\boxed{\sf{Area \: of \: \triangle \: = \dfrac{1}{2} \times Base \times Height}}}}} \\ \\ :\implies \sf Area \: of \: \triangle \: = \dfrac{1}{2} \times Base \times Height \\ \\ :\implies \sf 400 \: = \dfrac{1}{2} \times a \times 2a \\ \\ :\implies \sf 400 \: = \dfrac{1}{2} \times 2a^{2} \\ \\ :\implies \sf 400 \: = \dfrac{1}{\cancel{2}} \times \cancel{2}a^{2} \\ \\ :\implies \sf 400 \: = 1 \times a^{2} \\ \\ :\implies \sf 400 \: = a^{2} \\ \\ :\implies \sf \sqrt{400} \: = a \\ \\ :\implies \sf 20 \: = a \\ \\ \sf \underline{Henceforth, \: base \: is \: 20 \: centimetres}$

~ Now let us find out the height of the triangle, by following the given steps:

$:\implies \sf Height \: = 2a \\ \\ :\implies \sf Height \: = 2(20) \\ \\ :\implies \sf Height \: = 2 \times 20 \\ \\ :\implies \sf Height \: = 40 \: cm \\ \\ \sf \underline{Henceforth, \: 40 \: centimetres \: is \: height}$