A rectangle of side 8cm\times 6cm and a rhombus
A rectangle of side 8cm × 6cm and a rhombus (side = 8cm, acute angle $ 60^\circ$ are joined along one 8 cm side. what’s the ratio of their areas (rectangle : rhombus)?
8 सेमी × 6 सेमी भुजा वाला एक आयत और एक समबाहु चतुर्भुज जिसकी भुजा = 8 सेमी और तीव्र कोण $60^\circ$ है,एक 8 सेमी की भुजा के अनुदिश जुड़े हुए है। उनके क्षेत्रफलों का अनुपात (आयत : समचतुर्भुज) ?
Detailed Solution & Logic
$ \sqrt{3} : 2 $
Area of rectangle:
$8 \times 6 = 48$
Area of rhombus:
$8^2 \times \sin 60^\circ = 64 \times \frac{\sqrt{3}}{2} = 32\sqrt{3}$
Now, ratio (rectangle : rhombus):
$48 : 32\sqrt{3}$
Simplify:
Divide by 16 → $3 : 2\sqrt{3}$
Rationalize:
$= \frac{3}{2\sqrt{3}} = \frac{3}{2\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{3\sqrt{3}}{6} = \frac{\sqrt{3}}{2}$
So,
$= \sqrt{3} : 2$
Answer: $\sqrt{3} : 2$
Similar Practice Questions
ABCD is a quadrilateral in which AB|| DC, and E and F are the mid points of the diagonals AC and BD, respectively. If AB = 12 cm, BC = 40 cm, DC = 30 cm, and AD = 45 cm, then what is the length ( in cm) of EF?
ABCD is a quadrilateral in which AB|| DC, and E and F are the mid...
If the surface area of a sphere
If the surface area of a sphere is 5544 $ \text cm^2$ , then find...
In a circle, angle subtended by chord AB at the center is $ 80^\circ$. What is the measure of angle $\angle $ACB, Where C lies on the circle?
In a circle, angle subtended by chord AB at the center is $ 80^\circ$. What...
A cubic box with a side length of 30 cm needs to be wrapped with decorative paper made of square pieces, each with a side of 6 cm.
A cubic box with a side length of 30 cm needs to be wrapped with...
The respective ratios between the numerical values of a curved surface area
The respective ratios between the numerical values of a curved surface area and the volume...
Find the area of a square
Find the area of a square whose diagonal is of 14 cm length. उस वर्ग...
A circle has a radius of 7 cm. Calculate
A circle has a radius of 7 cm. Calculate the length of an arc that...