MATH SOLVE

3 months ago

Q:
# A rectangular pool 12 meters by 8 meters is surrounded by a walkway of width x meters. Atwhat value of x will the area of the walkway equal the area of the pool?

Accepted Solution

A:

Answer:x=3 metersStep-by-step explanation:step 1Find the area of the rectangular pool[tex]A=LW[/tex]we have[tex]L=18\ m\\W=12\ m[/tex]substitute[tex]A=18(12)=216\ m^2[/tex]step 2Find the area of rectangular pool including the area of the walkwayLetx ----> the width of the walkwaywe have[tex]L=(18+2x)\ m\\W=(12+2x)\ m[/tex]substitute[tex]A=(18+2x)(12+2x)[/tex]step 3Find the area of the walkwayTo find out the area of the walkway subtract the area of the pool from the area of rectangular pool including the area of the walkwayso[tex]A=(18+2x)(12+2x)-216[/tex]step 4Find the value of x if the area of the walkway equal the area of the poolso[tex](18+2x)(12+2x)-216=216[/tex]Solve for x[tex](18+2x)(12+2x)=432\\216+36x+24x+4x^{2}=432\\4x^{2} +60x-216=0[/tex]Solve the quadratic equation by graphingThe solution is x=3 meterssee the attached figure