A rectangle of side 8 cm × 6 cm and a rhombus (side = 8 cm, acute angle 60°) are joined along one 8 cm side. What's the ratio of their areas (rectangle : rhombus)?
\(\sqrt{3} : 2\)
Area of the rectangle = 8 × 6 = 48 cm2.
Area of a rhombus = \(a^2 \sin\theta = 8^2 \times \sin 60^\circ = 64 \times \frac{\sqrt{3}}{2} = 32\sqrt{3}\) cm2.
Ratio = \(48 : 32\sqrt{3} = 3 : 2\sqrt{3}\). Dividing both terms by \(\sqrt{3}\) gives \(\sqrt{3} : 2\).
Hence, the ratio of the areas (rectangle : rhombus) is \(\sqrt{3} : 2\).
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Important Questions from 2-D Mensuration
- The length of a rectangular plot is $(x^2 + xy + y^2)$ m and its breadth is $(x^2 - 5xy - y^2)$ m.
Find its perimeter, when $x = 1$ and $y = -1$. - The ratio between the perimeter and breadth of a rectangle is 3: 1. If the area of the rectangle is $98 \text{ cm}^2$, find the perimeter (in cm) of the rectangle.
The shorter side of a rectangle is 15 cm less than the longer side. The numerical value of its area is equal to 5 times the numerical value of its perimeter. What is the length (in cm) of its longer side?
- In a circle of radius 10.5 cm, if the angle of a sector is $\frac{2\pi}{3}$, then the perimeter of the sector is (in cm):
(Take $\pi = \frac{22}{7}$) - Find the circumference (in m) of the largest circle that can be inscribed in a rectangle whose dimensions are given as 114 m and 63 m.
Take $\pi = \frac{22}{7}$
