(A) Let the breadth of the rectangle be $x \,cm$.According to the problem, the length is $1.5$ times the breadth, so length $= 1.5x \,cm$.The perimete

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Length $= 30 \,cm$, Breadth $= 20 \,cm$

(A) Let the breadth of the rectangle be $x \,cm$.According to the problem, the length is $1.5$ times the breadth, so length $= 1.5x \,cm$.The perimeter of a rectangle is given by the formula $P = 2 \times (\text{length} + \text{breadth})$.Given $P = 100 \,cm$, we have $100 = 2 \times (1.5x + x)$.$100 = 2 \times (2.5x)$.$100 = 5x$.$x = 20 \,cm$.Therefore, the breadth is $20 \,cm$ and the length is $1.5 \times 20 = 30 \,cm$.

Class 10 Mathematics Pair of Linear Equations in Two Variables Mix Examples - Pair of Linear Equations in Two Variables

Medium

The length of a rectangle is one and a half times its breadth. If the perimeter of the rectangle is $100 \,cm$, find the length and the breadth of the rectangle.

A
Length $= 30 \,cm$, Breadth $= 20 \,cm$
B
Length $= 40 \,cm$, Breadth $= 10 \,cm$
C
Length $= 25 \,cm$, Breadth $= 25 \,cm$
D
Length $= 35 \,cm$, Breadth $= 15 \,cm$

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Pair of Linear Equations in Two Variables

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Mix Examples - Pair of Linear Equations in Two Variables

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The length of a rectangle is one and a half times its breadth. If the perimeter of the rectangle is $100 \,cm$, find the length and the breadth of the rectangle.

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The sum of the digits of a two-digit number is $13$. The number obtained by interchanging the digits is $9$ more than the original number. Find the original number.

If the lines given by $3x + 2ky = 2$ and $2x + 5y + 1 = 0$ are parallel,then the value of $k$ is

The length of a rectangle is $5$ less than twice its breadth. If its perimeter is $110,$ find the area of the rectangle. Use the cross-multiplication method for the solution.

If the following pair of equations is consistent (unique solution),then find the value of $k$:$x - ky = 2$$3x + 2y = -5$

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If the following pair of equations is consistent (unique solution),then find the value of $k$:
$x - ky = 2$
$3x + 2y = -5$