Instructions

Each of the questions given below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements. Give answer

Question 133

What will be the total cost of fencing a rectangular plot ?
I. The area of plot is 1134 sq. metre. The length of plot is 15 metre more than its breadth.
II. The cost of fencing is Rs. 180 per metre.

Solution

We need both dimensions and cost of fencing to answer the question. Thus, we require both statements.

Let breadth of the plot = $$x$$ m

=> Length = $$(x + 15)$$ m

=> Area of plot = $$x (x + 15) = 1134$$

=> $$x^2 + 15x - 1134 = 0$$

=> $$x^2 + 42x - 27x - 1134 = 0$$

=> $$x (x + 42) - 27 (x + 42) = 0$$

=> $$(x + 42) (x - 27) = 0$$

=> $$x = 27 , -42$$

As length of the plot cannot be negative => Breadth = $$x = 27$$ m

=> Length = $$27 + 15 = 42$$ m

Perimeter = $$2 (42 + 27) = 2 \times 69$$

= $$138$$ m

$$\therefore$$ Cost of fencing = $$138 \times 180$$

= Rs. $$24,840$$

Thus, Both statements together are required to answer the question.


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