Question : The length of the diagonals of a rhombus is 40 cm and 60 cm. What is the length of the side of the rhombus?
Option 1: $50 \sqrt{3} \ \text{cm}$
Option 2: $20 \sqrt{3}\ \text{cm}$
Option 3: $10 \sqrt{13}\ \text{cm}$
Option 4: $40 \sqrt{13}\ \text{cm}$
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Correct Answer: $10 \sqrt{13}\ \text{cm}$
Solution : Let's denote the length of the side of the rhombus as $s$ and the diagonal as $d1$ and $d2$. According to the given information, the diagonals of the rhombus are 40 cm and 60 cm. These diagonals divide the rhombus into four congruent right-angled triangles. Using the Pythagorean theorem, we can write the following equation for one of the right-angled triangles: $(\frac{d1}{2})^2 + (\frac{d2}{2})^2 = (s)^2$ Simplifying this equation: ⇒ $(\frac{40}{2})^2 + (\frac{60}{2})^2 = (s)^2$ ⇒ $(20)^2 + (30)^2 = (s)^2$ ⇒ $s^2 = 1300$ ⇒ $s = \sqrt{1300}$ ⇒ $s = 10\sqrt{13}\ \text{cm}$ Hence, the correct answer is $10\sqrt13\ \text{cm}$.
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Question : The length of each side of a rhombus is equal to the length of the side of a square whose diagonal is $40\sqrt2$ cm. If the length of the diagonals of the rhombus is in the ratio $3:4$, then its area ( in cm2) is:
Question : If the diagonals of a rhombus are 10 cm and 24 cm, then what is the perimeter of the rhombus?
Question : If one diagonal of a rhombus is equal to its side, then the diagonals of the rhombus are in the ratio of:
Question : PQRS is a square with a side of 10 cm. A, B, C, and D are mid-points of PQ, QR, RS, and SP, respectively. Then, the perimeter of the square ABCD so formed is:
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