Question

Morgan has a deck that measures 5 feet by 4 feet. She wants to increase each dimension by equal lengths so that its area is increased by 50%. By how much should she increase each dimension?

Answer 1

...initial area: 4*5 = 20ft²

she would like to increase this area by 50% so that it is then 20+(20*50)/100=30ft²

x" the increase in feet

the width 4 feet becomes (4+x)

the length 5 feet becomes (5+x)

A =(4+x)(5+x)= 20+4x+5x+x² = x²+9x+20

we calculate x:

x²+9x+20=30

x²+9x+20-30=0

x²+9x-10=0

b²-4ac = 9²-4(1*-10)=121

Δ=121

(-b-√Δ)/2 = (-9-11)/2=-10

(-b+√Δ)/2 = (-9+11)/2=1

a length is never negative, x=1

it must increase each dimension by 1 foot so that the surface of the terrace is increased by 50%.