Advertisements
Advertisements
प्रश्न
Lengths of diagonals of a rhombus ABCD are 16 cm and 12 cm. Find the side and perimeter of the rhombus.
Advertisements
उत्तर
ABCD is a rhombus.
Here, segment AC and segment BD are the diagonals of the rhombus ABCD.
l(AC) = 16 cm and l(BD) = 12 cm.
Diagonals of a rhombus are perpendicular bisectors of each other.
∴ m∠AOD = 90°
Also, l(OA) = `1/2l(AC) = 1/2 xx 16 = 8 cm`
l(OD) = `1/2l(BD) = 1/2`× 12 = 6 cm
In right ∆AOD,
l(AD)2 = l(OA)2 + l(OD)2 ...[Pythagoras theorem]
⇒ l(AD)2 = (8)2 + (6)2
⇒ l(AD)2 = 64 + 36 = 100
⇒ l(AD) = \[\sqrt{100}\] = 10 cm
All sides of a rhombus are equal.
∴ Perimeter of the rhombus ABCD = 4 × Side of a rhombus = 4 × 10 = 40 cm
Thus, the side and perimeter of the rhombus are 10 cm and 40 cm, respectively.
संबंधित प्रश्न
Can the following figure be parallelogram. Justify your answer.
In the following figure GUNS and RUNS are parallelogram. Find x and y.
In the following figure RISK and CLUE are parallelograms. Find the measure of x.
Find the angles marked with a question mark shown in Fig. 17.27
Which of the following statement is true for a rhombus?
It has only two pairs of equal sides.
Which of the following statement is true for a rhombus?
It is a parallelogram.
Which of the following statement is true for a rhombus?
It can be a square.
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.
Identify all the quadrilateral that have Four sides of equal length
Construct a rhombus whose side is 5 cm and one angle is of 60°.
