Finding Rectangle Sides from Ratio and Perimeter
Let the sides of the rectangle be $3x$ and $4x$ since they are in the ratio 3:4.
The formula for the perimeter of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width.
Given the perimeter $P = 42$ cm:
$2(3x + 4x) = 42$
$2(7x) = 42$
$14x = 42$
Solving for $x$:
$x = \frac{42}{14} = 3$
Now, calculate the actual lengths of the sides:
- Width = $3x = 3 \times 3 = 9$ cm
- Length = $4x = 4 \times 3 = 12$ cm
Calculating Rectangle Diagonal Length
The diagonal of a rectangle can be calculated using the Pythagorean theorem, where the diagonal ($d$) is the hypotenuse, and the sides ($l$ and $w$) are the other two sides of a right-angled triangle.
The formula is $d^2 = l^2 + w^2$.
Substitute the calculated side lengths:
$d^2 = (12 \text{ cm})^2 + (9 \text{ cm})^2$
$d^2 = 144 \text{ cm}^2 + 81 \text{ cm}^2$
$d^2 = 225 \text{ cm}^2$
Taking the square root to find the diagonal:
$d = \sqrt{225 \text{ cm}^2}$
$d = 15 \text{ cm}$
Therefore, the length of the diagonal is 15 cm.
Similar Questions
- A square is inscribed in a circle which is inscribed in an equilateral triangle. If one side of the triangle is $x$, then the area of square is:
- A path around the inner side of a rectangular park measuring $37\text{ m} \times 30\text{ m}$ occupies $570\text{ m}^{2}$. What is the width of the path?
- Four cows are tethered to the four corners of a square field of length 28 m so that each cow can just touch the two cows in the adjacent corners. If the grass in the area inside the square field that was accessible to the cows was enough to feed them for 22 days, for how many days would the grass that is beyond the reach of these cows be able to feed them if someone cuts it and leaves it inside the grazable parts? [Use $\pi = 22/7$]
- What is the area of a rhombus, whose sides are 25 cm and one of the diagonals is 14 cm?
- A sector of a circle has a radius of $18\text{ cm}$ and a central angle of $125^\circ$. What will be its approximate perimeter?
(Use $\pi = \frac{22}{7}$) - 30 ml paint is required to paint a circular plate of 20 cm radius. How much paint is required to paint a similar plate of radius 80 cm?
- If the length and the perimeter of a rectangle are in the ratio of 3 : 20, then its length and breadth will be in the ratio of:
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- There is a regular hexagon of side 5 cm. Find its area.
- The length of a rectangle is three-fifths of the radius of a circle. The radius of the circle is equal to twice the side of a square, whose area is 3025 sq. units. The breadth of the rectangle is one-fifth of the side of the square. What is the area (in sq. units) of the rectangle?
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 $\pi = \frac{22}{7}$
