Question

the area of a rectangle is 54 cm. The length is 2 cm more than x and the width is 5 cm less than twice x. Slove for x. round your answer to the nearest whole number.

Answer 1

area=LW
54=LW
L is 2 more than x L=2+x
w is 5 less than 2x W=-5+2x



54=LW
L=2+x
W=-5+2x
input
54=(2+x)(-5+2x)
distribute/FOIL
54=-10+4x-5x+2x^2
add like terms
54=-10-x+2x^2
minus 54
2x^2-x-64=0
quadratic formula
x=
`\frac{ -b+/-\sqrt{b^(2)-4ac} }{2a}`
x=
`\frac{ -(-1)+/-\sqrt{(-1)^(2)-4(2)(-64)} }{2(2)}`
x=
`( 1+/-√(1-(-256)) )/(4)`
x=
`( 1+/-√(1-(-256)) )/(4)`
x=4.257 or -3.75
we disregard the negative one because that would make legnth and width negative


x=4 (rounded)