Advertisements
Advertisements
Question
The diagonals of a quadrilateral are of lengths 6 cm and 8 cm. If the diagonals bisect each other at right angles, what is the length of each side of the quadrilateral?
Advertisements
Solution
\[\text{ Let the given quadrilateral be ABCD in which diagonals AC is equal to 6 cm and BD is equal to 8 cm }. \]
\[\text{ Also, it is given that the diagonals bisect each other at right angle, at point O }. \]
\[ \therefore AO = OC = \frac{1}{2}AC = 3 cm\]
\[\text{ Also }, OB = OD = \frac{1}{2}BD = 4 cm\]
\[\text{ In right }\bigtriangleup AOB: \]
\[ {AB}^2 = {OA}^2 + {OB}^2 \]
\[ \Rightarrow {AB}^2 = (9 + 16) {cm}^2 \]
\[ \Rightarrow {AB}^2 = 25 {cm}^2 \]
\[ \Rightarrow AB = 5 cm\]
\[\text{ Thus, the length of each side of the quadrilateral is 5 cm } . \]
\[\]
RELATED QUESTIONS
In the following figure RISK and CLUE are parallelograms. Find the measure of x.
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
The sum of two opposite angles of a parallelogram is 130°. Find all the angles of the parallelogram.
In the following Figure ABCD is a arallelogram, CE bisects ∠C and AF bisects ∠A. In each of the following, if the statement is true, give a reason for the same:
(i) ∠A = ∠C
(ii) \[\angle FAB = \frac{1}{2}\angle A\]
(iii) \[\angle DCE = \frac{1}{2}\angle C\]
(iv) \[\angle CEB = \angle FAB\]
(v) CE || AF
Which of the following statement is true for a rhombus?
Its diagonals bisect each other at right angles.
Fill in the blank, inthe following, so as to make the statement true:
A rhombus has all its sides of ...... length.
ABCD is a rhombus. If ∠ACB = 40°, find ∠ADB.
If the diagonals of a rhombus are 12 cm and 16cm, find the length of each side.
ABCD is a rhombus and its diagonals intersect at O.
(i) Is ∆BOC ≅ ∆DOC? State the congruence condition used?
(ii) Also state, if ∠BCO = ∠DCO.
If a diagonal of a quadrilateral bisects both the angles, then it is a ______.
