Question

A right angle triangle is isosceles. If the square of the hypotenuse is 50m², What is the length of equal sides?

Answer 1

GIVEN QUESTION -

A right angle triangle is isosceles. If the square of the hypotenuse is 50m², What is the length of equal sides?

REQUIRED ANSWER -

GIVEN -

• A right angled triangle is isosceles

• hypotenuse is 50 m²

• the other sides are equal

TO FIND -

• length of equal sides

SOLUTION -

We know that the hypotenuse is 50 m² and the other sides are equal, so let the equal sides be x

DIAGRAM -

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf x}\put(2.8,.3){\large\bf x}\put(4.2,2.5){\large\bf 50}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\end{picture}$

Now according to the question we need to apply Pythagoras theorem ,

According to the Pythagoras theorem:-

$\star \: \sf {Hypotenuse}^{2} + {Perpendicular}^{2} + {Base}^{2}$

$\Longrightarrow \sf 50 = (x)^2 + (x)^2$

$\Longrightarrow \sf 50 = x^2 + x^2$

$\Longrightarrow \sf 50 = 2 x^2$

$\Longrightarrow \sf x^2 = \dfrac{50}{2}$

$\Longrightarrow \sf x^2 = 25$

$\Longrightarrow \sf x = \sqrt{25}$

$\Longrightarrow \sf x = 5m$

• Therefore, A right angled triangle is isosceles . if the hypotenuse is 50 m² , Then is the length of equal sides will be 5 m .

★ Note :- Kindly view this answer from web to see the highlighted diagram mentioned in the answer.

Answer 2

Step-by-step explanation:

$GIVEN QUESTION -</p><p></p><p>A right angle triangle is isosceles. If the square of the hypotenuse is 50m², What is the length of equal sides?</p><p></p><p>REQUIRED ANSWER -</p><p></p><p>GIVEN -</p><p></p><p>• A right angled triangle is isosceles</p><p></p><p>• hypotenuse is 50 m²</p><p></p><p>• the other sides are equal</p><p></p><p>TO FIND -</p><p></p><p>• length of equal sides</p><p></p><p>SOLUTION -</p><p></p><p>We know that the hypotenuse is 50 m² and the other sides are equal, so let the equal sides be x</p><p></p><p>DIAGRAM -</p><p></p><p>\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf x}\put(2.8,.3){\large\bf x}\put(4.2,2.5){\large\bf 50}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\end{picture}</p><p></p><p>Now according to the question we need to apply Pythagoras theorem ,</p><p></p><p>According to the Pythagoras theorem:-</p><p></p><p>\star \: \sf {Hypotenuse}^{2} + {Perpendicular}^{2} + {Base}^{2}⋆Hypotenuse2+Perpendicular2+Base2</p><p></p><p>\Longrightarrow \sf 50 = (x)^2 + (x)^2⟹50=(x)2+(x)2</p><p></p><p>\Longrightarrow \sf 50 = x^2 + x^2⟹50=x2+x2</p><p></p><p>\Longrightarrow \sf 50 = 2 x^2⟹50=2x2</p><p></p><p>\Longrightarrow \sf x^2 = \dfrac{50}{2}⟹x2=250</p><p></p><p>\Longrightarrow \sf x^2 = 25⟹x2=25</p><p></p><p>\Longrightarrow \sf x = \sqrt{25}⟹x=25</p><p></p><p>\Longrightarrow \sf x = 5m⟹x=5m</p><p></p><p>• Therefore, A right angled triangle is isosceles . if the hypotenuse is 50 m² , Then is the length of equal sides will be 5 m .</p><p></p><p>★ Note :- Kindly view this answer from web to see the highlighted diagram mentioned in the answer.</p><p></p><p>$