Discussion

A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?

Answer: D

Turn the two facts into a sum and a product.

\[ 2(l + b) = 50 \quad\Longrightarrow\quad l + b = 25 \]

\[ lb = 150 \]

So \( l \) and \( b \) are the roots of

\[ x^{2} - 25x + 150 = 0 \quad\Longrightarrow\quad (x - 15)(x - 10) = 0 \]

\[ l = 15 \text{ m}, \qquad b = 10 \text{ m} \]

Checking the options directly also works: only 15 and 10 give both a sum of 25 and a product of 150.

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