Question

the length of two sides of a right triangle are equal. the square of the hypotenuse is 800 CM. find the length of each side​

Answer 1

ATQ,

The length of two sides of the right angle triangle are equal.

Let the equal sides of the right angle triangle be x each (base and perpendicular) -------(i)

Given square of the hypotenuse is 800cm.

➡ hypotenuse² = 800cm -------(ii)

By Pythagoras theorem, we get

➡ hypotenuse² = base² + perpendicular²

➡ 800cm = x² + x² (from equation (i) and (ii))

➡ 800cm = 2x²

➡ x² = 800/2

➡ x² = 400

➡ x = √400

➡ x = 20cm

Hence, the length of other sides is 20cm each.

VERIFICATION :-

LHS :-

= 800cm

RHS :-

= (20)² + (20)²

= 400cm + 400cm

= 800cm. Hence verified!

Answer 2

$\huge\underline\mathfrak\pink{Answer}$

The length of other two sides of a triangle are 20cm and 20cm.

______________________

$\huge\underline\mathfrak\pink{Explanation}$

The two sides of the right angled triangle are equal. Therefore, it is a isosceles right angled triangle.

Also, the square of hypotenuse is 800cm ( Given ).

Let the one side be x, so another one is also be x as both sides are equal ( given ).

According to Pythagoras theorem,

Hypotenuse² = base² + perpendicular²

800 = x² + x²

800 = 2x²

x² = 800/2

x² = 400

x = ±√400

x = ±20

But length of side can't ne negative.

Therefore, the length of other side be 20 cm.

_________________________

$\huge\underline\mathfrak\pink{Verification}$

H² = B² + B³

800 = 20² + 20²

800 = 400 + 400

800 = 800

________________________

Hence verified!