waecmaths question:
The lengths of the adjacent sides of a right-angled triangle are xcm, (x – 1)cm. If the length of the hypotenuse is $\sqrt{13}cm$ find the value of x
Option A:
2
Option B:
3
Option C:
4
Option D:
5
waecmaths solution:
$\begin{align} & \text{Using pythagoras theorem} \\ & {{x}^{2}}+{{(x-1)}^{2}}={{(\sqrt{13})}^{2}} \\ & {{x}^{2}}+{{x}^{2}}-2x+1=13 \\ & 2{{x}^{2}}-2x-12=0 \\ & {{x}^{2}}-x-6=0 \\ & (x-3)(x+2)=0 \\ & x=3\text{ }\!\!\{\!\!\text{ }x\text{ cannot be a negative integer }\!\!\}\!\!\text{ } \\\end{align}$
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