A geometry problem by Ez Ra

Geometry Level pending

Find the length of the base of a parallelogram with an area of 48 square units and the base is represented by (x+3) and its altitude by (x+1)

7 Units 3 Units 6 Units 8 Units

Ez Ra by Ez Ra , 76, Philippines

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1 solution

Áron Bán-Szabó
Jul 14, 2017

48 = ( x + 3 ) ( x + 1 ) = x 2 + 3 x + x + 3 = x 2 + 4 x + 3 = x 2 + 4 x + 4 − 1 = ( x + 2 ) 2 − 1 ⇒ 49 = ( x + 2 ) 2 Note that x + 1 > 0 7 = x + 2 5 = x \begin{aligned} 48 & = (x+3)(x+1) \\ & = x^2+3x+x+3 \\ & = x^2+4x+3 \\ & = x^2+4x+4-1 \\ & = (x+2)^2-1 \\ \Rightarrow 49 & = (x+2)^2 & \text{Note that} \ x+1>0 \\ 7 & = x+2 \\ 5 & = x \end{aligned}

So the length of the base is equal to x + 3 = 5 + 3 = 8 x+3=5+3=\boxed{8} .

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