Question

The
base of a Triangle is thrice its height. If the area
of Triangle is 486cm², find the base and height of the
triangle​

Answer 1

Answer:

height= 18cm

Base=  54cm

Explanation:

Let the height be h

therefore,  Base= 3h

$area = \frac{1}{2} X b X h\\=> 486cm^{2} = \frac{1}{2} X b X h\\\\=> 486cm^{2} = \frac{1}{2} X 3h X h\\\=> 486cm^{2} = \frac{1}{2} X 3h^{2} \\=\frac{486 X 2}{3} = h^{2} \\\\=> 162X2 = h^{2} \\\=> 324 = h^{2}\\=> \sqrt{324}cm = h\\=> h = 18cm\\\\Therefore, Height = h = 18cm\\And, Base= 3h = 3 X 18cm = 54cm$

Mark this as brainliest, please

Answer 2

Given: The base of a triangle is thrice its height and the area of triangle is 486 cm².

Need to find: The base and height of the triangle?

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━

❒ Let us consider that, the height of the triangle be x cm.

⠀⠀⠀

Given that,

• The base of a triangle is thrice its height.

⠀

Therefore,

⠀

$\sf{:\implies Base_{(triangle)} = 3x}$

⠀

◗ Let's Head to the Question now:

⠀

We know that, if we are given with the height of triangle and base of triangle, we have the required formula, that is,

⠀

$\sf{:\implies Area_{(triangle)} = \dfrac{1}{2} \times b \times h}$

⠀

By using the formula of area of rectangle and Substituting all the given values in the formula, we get:

⠀

$\sf{: \implies 486 = \dfrac{1}{2} \times 3x \times x}$

⠀⠀⠀

$\sf{: \implies 486 \times 2 = 1 \times 3x \times x}$

⠀⠀⠀

$\sf{: \implies 972 = 1 \times 3x \times x}$

⠀⠀⠀

$\sf{: \implies 972 = 3x \times x}$

⠀⠀⠀

$\sf{: \implies 972 = 3{x}^{2} }$

⠀⠀⠀

$\sf{: \implies {x}^{2} = \cancel{\dfrac{972}{3} }}$

⠀⠀⠀

$\sf{: \implies {x}^{2} = 324} \\ \\ \\ \sf{: \implies x = \sqrt{324} }$

⠀⠀⠀

$\sf{: \implies \boxed{\frak{ \pink{x = 18}}}}$

⠀

Hence, the height and base of the triangle are:

• Height of triangle, x = 18 cm.

• Base of triangle, 3x = 3(18) = 54 cm.

⠀

$\sf{\therefore \underline{The \: base \: and \: height \: of \: triangle \: are \: \textsf{\textbf{18 cm}} \: and \: \textsf{\textbf{54 cm}} \: respectively.}}$