The length of a rectangle exceeds its breadth | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the breadth of the rectangle be $x \, cm$. Then,the length of the rectangle is $(x + 3) \, cm$. According to the problem,the numerical value o

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) Let the breadth of the rectangle be $x \, cm$. Then,the length of the rectangle is $(x + 3) \, cm$. According to the problem,the numerical value of the area is equal to the numerical value of the perimeter. Area $= 	ext{Length} 	imes 	ext{Breadth} = x(x + 3) \, cm^2$. Perimeter $= 2(	ext{Length} + 	ext{Breadth}) = 2(x + 3 + x) = 2(2x + 3) = (4x + 6) \, cm$. Equating the two: $x(x + 3) = 4x + 6$. $x^2 + 3x = 4x + 6$. $x^2 - x - 6 = 0$. Factoring the quadratic equation: $(x - 3)(x + 2) = 0$. This gives $x = 3$ or $x = -2$. Since the breadth cannot be negative,the breadth is $3 \, cm$.

The length of a rectangle exceeds its breadth by $3 \, cm$. If the numerical values of the area and the perimeter of the rectangle are equal,then the breadth is ...... $cm$.

Similar Questions

The perimeter of an equilateral triangle is $72 \sqrt{3} \text{ cm}$. Find its height in meters.

An equilateral triangle is cut up into smaller equilateral triangles with side $1/6$ of the original. Find the number of triangles thus formed?

How many cubes of edge $3\, cm$ can be cut out of a wooden cube of edge $9\, cm$?

Height of an equilateral triangle is $6 \, cm$. Find its side? (in $cm$)

$A$ circular wire of length $168 \text{ cm}$ is cut and bent in the form of a rectangle whose sides are in the ratio of $5:7$. What is the length (in $\text{cm}$) of the diagonal of the rectangle?

Vedclass Test Series

Exam Paper Generator

Online Exam Module