Question

If a and b are two sides of a parallelogram and c and d are the diagonals then :-
(1) c2 + d2 = a2 + b2
(2) c2 + d2 = 2 (a2 + b2)
(3) c2 – d2 = a2 – b2
(4) c2 – d2 = 2 (a2 – b2)

Answer 1

Answer on Question # 41701 - Physics, Mechanics | Kinamatics | Dynamics

1. If $a$ and $b$ are two sides of a parallelogram and $c$ and $d$ are the diagonals then:

(1) $c2 + d2 = a2 + b2$

(2) $c2 + d2 = 2(a2 + b2)$

(3) $c2 - d2 = a2 - b2$

(4) $c2 - d2 = 2(a2 - b2)$.

Solution.

If $a$ and $b$ are two sides of a parallelogram and $c$ and $d$ are the diagonals, then $\vec{a} + \vec{b} = \vec{c}$, $\vec{a} - \vec{b} = \vec{d}$, where the directions of the vectors can be chosen in such a way that direction of each vector coincides with the direction of an appropriate section.

Let bring the equalities to the square:

$$a^2 + 2(\vec{a} \vec{b}) + b^2 = c^2, \quad a^2 - 2(\vec{a} \vec{b}) + b^2 = d^2.$$

The sum of this equalities is $2(a^2 + b^2) = c^2 + d^2$.

Answer: the right answer is the second one.

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