Discussion

Explanation:

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Area ∆ABC = $\frac{1}{2}\times x\times h$ = 60 sq.cm.
⇒ x × h = 120   …(1)

Also, in right triangle ADC,
13² = ${\left(\frac{x}{2}\right)}^2$ + h²

⇒ x² + 4h² = 676

⇒ x² + 4 × (120/x)² = 676

It would be better to check options now.

∴ x = 10 or 24, are the roots of the above equation.

Hence, option (d).

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