Question

Under what coditions do the following metals react with water- K, Ca,  Mg,  Zn,Fe, and Cu.Give the necessary chemical equations.

Answer 1

Explanation:

Given

ABCD is a quadrilateral

∠B = 90°

∠D = 90°

To find

2 AC² - AB² = BC² + CD²+ DA²

Solution

In ∆ABC

By pythagoras theorem,

AC² = AB² + BC² ---- (1)

In ∆ADC

By pythagoras theorem,

AC² = CD² + DA² --- (2)

Add (1) and (2),

AC² + AC² = AB² + BC² + CD² + DA²

2AC² = AB² + BC² + CD² + DA²

2AC² - AB² = BC² + CD² + DA²

Hence, proved.

Figure :-

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Know More :-

Pythagoras theorem :-

In a right - angled triangle, the sum of the square of the hypotenuse is equal to the sum of the square of the other two sides.

• H² = P² + B²

where,

H = hypotenuse (the longest side)

P = perpendicular

B = base

Converse of pythagoras theorem :-

If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right angled triangle.