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Mathematics · Quadratic Equations · NCERT Examples

Example 6

A complete, independently verified solution for NCERT Example 6.

Mathematics · Chapter 4 · NCERT Examples

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NCERT Example

Example 6

factorisation · word problem

Find the dimensions of a prayer hall whose breadth is x metres, length is 2x + 1 metres, and area is 300 m².

Solution

x(2x+1)=300⇒2x2+x−300=0x(2x+1)=300\Rightarrow2x^2+x-300=0
2x2−24x+25x−300=02x^2-24x+25x-300=0
(x−12)(2x+25)=0(x-12)(2x+25)=0
x=12orx=−252x=12 \text{or} x=-\frac{25}{2}

Breadth cannot be negative, so −12.5 is rejected. The length is 2(12) + 1 = 25 m.

Final answer

Breadth = 12 m and length = 25 m.