Question

Suppose $A + L = 130$, where $A$ is the area of a rectangle and $L$ is the length of one side of a rectangle. If the length of the other side of the rectangle is $6$ units, what is the value of A?
A. $100$
B. $111.42$
C. $122.28$
D. $125$
E. $130$

Answer 1

Hint:Here in this question, we are given a relationship between the area and length of a rectangle. We are also given the length of one dimension of the rectangle in the problem. So, we express area in terms of length of one dimension and from an equation.Then, we solve the equation to find the length of the dimension.

Formula used:
The area of the rectangle using the formula
$A = l \times b$
where $l$ and $b$ are the length and breadth of the rectangle.

Complete step by step answer:
A rectangle is a two dimensional shape with all four angles equal to ${90^ \circ }$ and opposite sides as equal. To determine the area of a rectangle, we have the standard formula $A = L \times B$ where L and B denote the length and breadth of the rectangle. The unit for the area is square units. So, we are given the relation in length and area of the rectangle as $A + L = 130$. Also, the breadth of a rectangle is given as $6$ units.

Now, we substitute the value of breadth in the formula for area of rectangle. Hence, we get,
$ \Rightarrow A = 6L$
Now, substituting the expression for area of rectangle in the given equation, we get,
$A + L = 130$
$ \Rightarrow 6L + L = 130$
$ \Rightarrow 7L = 130$
Dividing both sides of the equation by $7$, we get,
$ \Rightarrow L = \dfrac{{130}}{7}$
So, the length of the rectangle is $\dfrac{{130}}{7}$ units.
Now, we find the area of the rectangle by putting in the values of length and breadth of the rectangle into the formula.
 So, $A = L \times B = \dfrac{{130}}{7} \times 6$
Simplifying the expression, we get,
$ \Rightarrow A = \dfrac{{780}}{7}$
$ \therefore A = 111.42$
Hence, the area of the rectangle is $111.42$ square units.

Therefore, the correct answer is option B.

Note: Generally the area is the region occupied by the thing. The area of a rectangle is defined as the region occupied by the quadrilateral region. We must know the formulae for area and perimeter of basic shapes like square, rectangle, parallelogram, circle, etc. We also must take care of the calculations while doing such questions. One must have a strong grip over concepts of transposition in order to solve equations formed in the problem.