Advertisements
Advertisements
Question
ABCD is a rhombus whose diagonals intersect at O. If AB = 10 cm, diagonal BD = 16 cm, find the length of diagonal AC.
Advertisements
Solution
\[\text{ We know that the diagonals of a rhombus bisect each other at right angles }. \]
\[ \therefore BO = \frac{1}{2}BD = (\frac{1}{2} \times 16) cm\]
\[ = 8cm\]
\[AB = 10 \text{ cm and }\angle AOB = 90°\]
\[\text{ From right } ∆ OAB: \]
\[ {AB}^2 = {AO}^2 + {BO}^2 \]
\[ \Rightarrow {AO}^2 = ( {AB}^2 -{BO}^2 )\]
\[ \Rightarrow {AO}^2 = (10 )^2 - (8 )^2 {cm}^2 \]
\[ \Rightarrow {AO}^2 = (100 - 64) {cm}^2 = 36 {cm}^2 \]
\[ \Rightarrow AO = \sqrt{36} cm = 6cm\]
\[ \therefore AC = 2 \times AO = (2 \times 6) cm = 12 cm\]
RELATED QUESTIONS
The following figure is parallelogram. Find the degree values of the unknowns x, y, z.
In the adjacent figure HOPE is a parallelogram. Find the angle measures x,y and z. State the geometrical truths you use to find them.
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
Which of the following statement is true for a rhombus?
Two of its angles are at right angles
Fill in the blank, inthe following, so as to make the statement true:
A square is a rhombus in which .....
Fill in the blank, inthe following, so as to make the statement true:
A rhombus has all its sides of ...... length.
The diagonals of a parallelogram are not perpendicular. Is it a rhombus? Why or why not?
Which of the following statement is true for a rectangle?
Its diagonals are equal and bisect each other.
Lengths of diagonals of a rhombus ABCD are 16 cm and 12 cm. Find the side and perimeter of the rhombus.
In rhombus ABCD;
(i) if ∠A = 74° ; find ∠B and ∠C.
(ii) if AD = 7.5 cm ; find BC and CD.
