Question

A right-angled triangle is isosceles. if the hypotenuse is of length equal to the square root of 50(in cm), what is the length of each of its legs?​

Answer 1

Answer:

Step-by-step explanation:

Given that the triangle is isosceles triangle and is right angled.

Side AB = Side BC [Since this is an isosceles triangle]

Let these two sides be x

According to Pythagores Theorem,

 $AC^{2} = AB^{2} + BC^{2}$

AC is $\sqrt{50}$ cm as it is the hypotenuse

  $(\sqrt{50})^{2}$$= x^{2} +x^{2}$

Adding like terms,

50 = $2x^{2}$

Transposing 2 to R.HS

$x^{2} = \frac{50}{2}$

Square root on both sides

$x = \sqrt{25}$

x= 5 cm

Therefore,

AB=BC=5 cm

Hope it helps,

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