Question

a right angled triangle is isosceles . if the hypotenuse is 50 m , what is the length of equal sides

Answer 1

Given,

A right angled triangle is isosceles . Hypotenuse is 50 m.

To find :

Length of equal sides .

Solution :

$\star$ Diagram :

$\setlength{\unitlength}{20 mm}\begin{picture}(6,6)\put(0,0){\line(0,1){1.1}}\put(0,0){\line(1,0){1.1}}\put(1.1,-0){\line(-9,1){1.1}}\put(-0,0.1){\line(1,0){0.1}}\put(0.1,0){\line(0,1){0.1}}\put(-0.1,1.2){\bf{A}}\put(-0.2,-0.2){\bf{B}}\put(1.1,-0.2){\bf{C}}\put(0.7,0.6){\bf{50 m}}\put(0.5,-0.2){\bf{y}}\put(-0.2,0.5){\bf{y}}\end{picture}$

We have, hypotenuse = 50 m

Let, base = perpendicular = y m

Now using pythagoras theorem,

⇒ Hypotenuse² = Base² + Perpendicular²

⇒ 50² = y² + y²

⇒ 2500 = 2y²

⇒ 2500/2 = y²

⇒ 1250 = y²

⇒ y = √1250

⇒ y = 35.36 m

Therefore,

Length of each equal side = 35.36 m

Answer 2

Given:-

• A right angle Triangle is isosceles.
• Hypotenuse = 50m

Find:-

• Length of Equal sides.

Diagram:

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(0.2,2.5){ \bf 'x' m }\put(2.8,0.6){ \bf 'x' m }\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,0.3){\large\bf C} \put(4,2.5){\bf 50m}\end{picture}$

Solution:-

we, know that in a isosceles Triangle two sides are equal.

So,

Let, the perpendicular = 'x' m

So, equal side = Base = 'x' m

Now, In ∆ABC

⌦ H² = P² + B²...........[Pythogoras Theorem]

⌦ AC² = AB² + BC²

Where,

• AC = 50m
• AB = 'x' m
• BC = 'x' m

• Substituting these values •

➻ 50² = x² + x²

➻ 2500 = 2x²

➻ 2500/2 = x²

➻ 1250 = x²

➻ √(1250) = x

➻ x = 35.355m(approx.)

➻ x = 35.36m

• So, the length of the equal sides of the right angled Triangle is 35.36m