The area of a rectangular plank is 4500 cm². The plank was broken into two pieces, one of which is a square and the other a rectangle. Find the dimensions of the square if the length of the broken off rectangle is 120 cm.

Accepted Solution

Answer:[tex]Xs=30cm[/tex] and [tex]As=900 cm^{2}[/tex]Step-by-step explanation:At=As+Ar; A=b.h and [tex]At=4500 cm^{2}[/tex], then:  At=(x+120)x so (x+120)x=4500, [tex]x^{2} +120x-4500=0[/tex] Applying cuadratic equation formula:[tex]\frac{120+-\sqrt{120^{2} -4.1.-4500} }{2} =-\frac{120+-\sqrt{14400+18000} }{2}= x1=30 and x2=-150, finally Xs=30cm, and As=900cm^{2}[/tex]