Question

3. The perimeter of a rectangle is numerically equal to the area of the rectangle. If the width of rectangle is
5×3/2m, find its length.​

Answer 1

Answer:

• The length of the rectangle is 30/11 m.

Step-by-step explanation:

Given that:

• The perimeter of a rectangle is numerically equal to the area of the rectangle.
• The width of the rectangle is 5 × 3/2m

To Find:

• The length of the rectangle.

Solution:

Width of the rectangle = 5 × 3/2m = 15/2 m

As we know that:

• Perimeter of rectangle = 2(Length + Breadth)
• Area of rectangle = Length × Breadth

According to the question:

⇢ Perimeter of the rectangle = Ar. of the rectangle

Substituting the values,

$\sf{\longmapsto2\left(L+\dfrac{15}{2}\right)=L\times\dfrac{15}{2}}$

Solving further,

$\sf{\longmapsto2L+15=\dfrac{15L}{2}}$

Transposing 2L from LHS to RHS and changing its sign,

$\sf{\longmapsto15=\dfrac{15L}{2}-2L}$

Subtracting,

$\sf{\longmapsto15=\dfrac{15L-4L}{2}}$

$\sf{\longmapsto15=\dfrac{11L}{2}}$

Transposing 2 from RHS to LHS and changing its sign,

$\sf{\longmapsto15\times2=11L}$

Multiplying,

$\sf{\longmapsto30=11L}$

Transposing 11 from RHS to LHS and changing its sign,

$\sf{\longmapsto\dfrac{30}{11}=L}$

$\bf{\longmapsto L=\dfrac{30}{11}}$

Hence,

• Length of the rectangle is 30/11 m.