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
From an outside point P, Two tangents, PA and PB, are drawn to a circle. A third tangent to the circle at a point Q intersects PA and PB at R and s respectively. If PA = 10 cm, What is the perimeter of $\delta Prs$?
From an outside point P, Two tangents, PA and PB, are drawn to a circle....
If the radius of a right circular cylinder is increased by 10 percent while its height remains constant, what is the percentage increase in its volume?
If the radius of a right circular cylinder is increased by 10 percent while its...
A right circular cone is cut into two parts of equal height by a horizontal plane.
A right circular cone is cut into two parts of equal height by a horizontal...
What is the area of a triangle with a base of 12 cm and a height of 8 cm?
What is the area of a triangle with a base of 12 cm and a...
Two circles have radii of 8 cm and 3 cm. The distance between their centers is 15 cm. What is the length of a direct common tangent?
Two circles have radii of 8 cm and 3 cm. The distance between their centers...
A circular jogging track has a radius of 50 m. A runner covers a curved path that subtends an angle of $120^\circ$ at the center. What is the length of the arc she runs?
A circular jogging track has a radius of 50 m. A runner covers a curved...
If PQ and PR are the two tangents to a circle with center O, and ∠QOR= $150^\circ$, then ∠QPR is equal to:
If PQ and PR are the two tangents to a circle with center O, and...