Question

antos
ight is Ilcm.
In a triangle the height is double the base and the area is 400 cm. Find the length of th
base and height.
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Answer 1

Appropriate Question :

• In a triangle the height is double the base and the area is 400 cm² . Find the length of the base and height.

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❍ Let's Consider the Length of Base of Triangle be x cm .

Given that ,

• The Height of Triangle is double of its base .

Therefore,

• Height of Triangle is 2x cm .

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{Area _{(Triangle} \:: \dfrac{1}{2} \times b \times h }\bigg\rgroup$

⠀⠀⠀⠀⠀Here b is the Base of Triangle , h is the Height of Triangle & Area of Triangle is 400 cm² .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \longmapsto \sf 400 = \dfrac{1}{2} \times x \times 2x$

$\qquad \longmapsto \sf 400 \times 2 = x \times 2x$

$\qquad \longmapsto \sf 800 = x \times 2x$

$\qquad \longmapsto \sf 800 = 2x^2$

$\qquad \longmapsto \sf \cancel {\dfrac{800}{2}} = x^2$

$\qquad \longmapsto \sf 400 = x^2$

$\qquad \longmapsto \sf \sqrt {400}= x$

$\qquad \longmapsto \sf 20 = x$

$\qquad \longmapsto \frak{\underline{\purple{\:x = 20 cm }} }\bigstar$

Therefore,

• Base of the Triangle is x = 20 cm .
• Height of the Triangle is 2x = 2(20) = 40 cm .

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \sf Base\:\:\& \:\:Height \:of\:Triangle \:are\:\bf 20\:cm\:\:\&\:\:40\:cm \sf ,respectively. }}$

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V E R I F I C A T I O N :

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{Area _{(Triangle} \:: \dfrac{1}{2} \times b \times h }\bigg\rgroup$

⠀⠀⠀⠀⠀Here b is the Base of Triangle , h is the Height of Triangle & Area of Triangle is 400 cm² .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \longmapsto \sf 400 = \dfrac{1}{2} \times 20 \times 40$

$\qquad \longmapsto \sf 400 = \dfrac{1}{\cancel {2}} \times 20 \times \cancel {40}$

$\qquad \longmapsto \sf 400 = 20 \times 20$

$\qquad \longmapsto \bf 400 cm^2 = 400 cm^2$⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\therefore {\underline {\bf{ Hence, \:Verified \:}}}$

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Answer 2

Let's Consider the Length of Base of Triangle be x cm .

Let's Consider the Length of Base of Triangle be x cm .Given that ,

Let's Consider the Length of Base of Triangle be x cm .Given that ,The Height of Triangle is double of its base .

Therefore,Height of Triangle is 2x cm.

WE KNOW THAT:

$area_{triangle} = \frac{1}{2} \times base \times hieght$

AND , AREA OF TRIANGLE is given

${400}^{2}cm$

️‍️

NOW BY USIY SUBSTITUTIONS METHOD

we get,

$=> \: 400 = \frac{1}{2} \times x \times 2x$

$=> \: 400 \times 2 = x \times 2x$

$=> \: 800 \times 2 {x}^{2}$

$\frac{800}{2} \: = {x}^{2}$

$400 = {x}^{2}$

$\sqrt{400} = x$

$x = 20$

=> the value of X = 20 cm.