Question:
If the area of a rhombus is \(24\text{ cm}^2\) and one of its diagonals is \(8\) cm, then the side of that rhombus (in cm) is
If the area of a rhombus is \(24\text{ cm}^2\) and one of its diagonals is \(8\) cm, then the side of that rhombus (in cm) is
Show Hint
In rhombus problems, after finding diagonals, use half-diagonals with Pythagoras theorem to find the side.
Updated On: Jul 15, 2026
- \(5\)
- \(6\)
- \(4\)
- \(\frac52\)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Concept:
Area of a rhombus:
\[
A=\frac12 d_1d_2
\]
where \(d_1,d_2\) are diagonals.
Also, diagonals bisect each other at right angles.
Step 1: Find the second diagonal.
Given: \[ A=24 \] \[ d_1=8 \] So: \[ 24=\frac12(8)(d_2) \] \[ 24=4d_2 \] \[ d_2=6 \]
Step 2: Use half diagonals to form a right triangle.
Half diagonals: \[ \frac{8}{2}=4 \] \[ \frac{6}{2}=3 \] Side of rhombus: \[ =\sqrt{4^2+3^2} \] \[ =\sqrt{16+9} \] \[ =\sqrt{25} \] \[ =5 \] Thus, the side of the rhombus is: \[ \boxed{5} \]
Step 1: Find the second diagonal.
Given: \[ A=24 \] \[ d_1=8 \] So: \[ 24=\frac12(8)(d_2) \] \[ 24=4d_2 \] \[ d_2=6 \]
Step 2: Use half diagonals to form a right triangle.
Half diagonals: \[ \frac{8}{2}=4 \] \[ \frac{6}{2}=3 \] Side of rhombus: \[ =\sqrt{4^2+3^2} \] \[ =\sqrt{16+9} \] \[ =\sqrt{25} \] \[ =5 \] Thus, the side of the rhombus is: \[ \boxed{5} \]
Was this answer helpful?
0
0
Top TG ICET Mathematical Ability Questions
- \[ \frac{\left(a^{\frac12}b^{-\frac16}\right)^3- \left(a^{\frac16}b^{\frac13}\right)^3} {a^{\frac12}-b^{\frac12}} = ? \]
- \[ 64^{\frac13} - 81^{\frac14} + 625^{\frac14} = ? \]
- If \(x:y=4:5\), then \((5x+4y):(10x-2y)=\ ?\)
- The ratio of milk and water in a can of 36 liters is \(3:1\). If 6 more liters of water is added, then the ratio of the milk and water will be:
- If \[ \sqrt{12+4\sqrt5} + \sqrt{16-4\sqrt7} = \sqrt{x}+\sqrt{y}, \] then find the value of \[ \sqrt{35xy}. \]
View More Questions
Top TG ICET Geometry Questions
- The least number of square tiles required to cover the floor of a room with dimensions \(24\) meters \(78\) cm \(\times\) \(27\) meters \(26\) cm is:
- What is the area of a rhombus (in sq.m.) whose perimeter is 40 m and one of its diagonals is 16 m?
- The dimensions of a brick and a wall are \(20\text{ cm} \times 10\text{ cm} \times 7.5\text{ cm}\) and \(25\text{ m} \times 2\text{ m} \times 0.75\text{ m}\) respectively. How many bricks (in thousands) are required to construct the wall?
- The volume of a cuboid is twice that of the volume of a cube. The dimensions of the cuboid are 9 cm, 8 cm, and 6 cm. If it costs ₹2.50 per sq.cm. for painting, the amount required to paint the surfaces of the cube (in rupees) is:
- The length and height of a godown are \(22\)m and \(6.5\)m respectively. If the area of four walls is \(442\) sq.m., then the breadth of the room in meters is:
View More Questions
Top TG ICET Questions
- What is the average of the integers 1, 2, 3, 4, and \(x\)? Statement (I): \(x\) is an even integer. Statement (II): \(x<10\)
- What is the average of \(x,y,z\) and \(t\)? Statement (I): \(x+z=12\) Statement (II): \(y+t=24\)
- What is the sum of the first 30 terms of an Arithmetic Progression? Statement (I): The common difference of the A.P. is 5. Statement (II): The first and the last terms are 2 and 60 respectively.
- In triangle \(ABC\), is \(\angle A\) obtuse? Statement (I): \(\angle C\) is acute. Statement (II): \(\angle B\) is obtuse.
- What is the circumference of the regular hexagon? Statement (I): The radius of the circumcircle of the hexagon is \(6\) cm. Statement (II): Each side of the hexagon subtends an angle of \(60^\circ\) at the centre.
View More Questions