Math, asked by BrainlyChallenger, 1 year ago

if the area of a right isosceles triangle is 50sq.m, (Hypotenuse)Are Nit Included In Equal) what is the length of the identical sides of a triangle

Answers

Answered by BrainlyKing5
2
\underline{\textbf{Hey Mate Here Is Your Answer }}

\underline{\textbf{Given That...}}

The Area Of A Right Isosceles Triangle Is 50{m}^{2} And it's Equal Sides Are It's Base And Height We Need To Find The Length Of The Equal Sides ..

So Now Let's Move For Solution\Longrightarrow

\underline{\textbf{Solution..}}

According To Question It's Said That In An Isosceles Triangle Both height And Base Are Equal ..\Longrightarrow

So Now Let\Longrightarrow

The Measure Of Height Be = H

And

The Height Of Breadth be = B

Now We Know That Area Of A Right Angled Triangle Is \Longrightarrow

\boxed{\mathbf{Area\: = \frac{1}{2} \times Base \times Height}}

Now In Question It's Given That Area Of Triangle = \mathbf{50 {m}^{2}}

So Now By This We Have \Longrightarrow

 \mathbf{ \frac{1}{2} \times base \: \times height = 50 {m}^{2} }

So Now Putting Values Of Base = B And Height = H

But According To Question This Both Measures Are Equal

\therefore \mathbf{Height = Base }

So Let Both Values Of Base = Height be = N

So Now Putting The Values Of Base And Height = N We Have \Longrightarrow

Thus We Have

 \mathbf{ \frac{1}{2} \times \: N \times N = 50 {m}^{2} } \:

Therefore Now Solving This Equation We Have..

 \mathbf{ \frac{1}{2} \times { (N)}^{2} = 50 {m}^{2} } \:

Now Taking 1/2 RHS We Have ..

 \mathbf{ { N}^{2} \: = 50 {m}^{2} \times 2}

That Is

 \mathbf{ { N}^{2} \: = \: 100 {m}^{2} }

Therefore At Last We Have

 \mathbf{ N\: = \: \sqrt{100 {m}^{2}} = 10m}

So Now We Have

\boxed{\mathbf{Base\: =\: Height\: =\: N \:=\: 10m}}

\underline{\textbf{Hence The Required Answer Is }}

\boxed{\boxed{\boxed{\mathbf{10m}}}}

\large{\mathcal{Thanks..}}
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