Question

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

Answer 1

$\underline{\textbf{Hey Mate Here Is Your Answer }}$

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

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

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

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

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

$\large{\mathcal{Thanks..}}$