Algebra 2 - Quadratic Equations- What are the length and width of Jasmine's rectangle?

Jasmine drew a rectangle which is 143 square mm. Ethan drew a rectangle inside of Jasmine's which is 35 square mm. Ethan's rectangle has a three mm border between his and Jasmine's rectangle. What are the length and width of Jasmine's rectangle?

A13 mm by 11 mm

B12 mm by 11 mm

C15 mm by 15 mm

D13 mm by 12 mm

E13 mm by 13 mm

F14 mm by 15 mm



Noah is trying to qualify for a race. A driver needs to complete 8 laps of a seven-mile track at an average speed of 105.66 mph to qualify. Noah has already completed the first three laps. His average speed so far is ninety-two mph. What must his average speed be for the rest of the race to qualify?

A Approximately 146 mph

B Approximately 96 mph

C Approximately 116 mph

D Approximately 136 mph

E Approximately 106 mph

F Approximately 126 mph

Algebra 2 - Quadratic Equations- What are the length and width of Jasmine's rectangle?
Let jw and jl be the length and width of Jasmine's rectangle, and ew and el be the length and width of Ethan's rectangle

We know:

jw * jl = 143



Solve for jw

jw = 143 / jl



We also know

ew * el = 35

ew = jw - 6

el = jl - 6



Plug in ew and el

ew * el = 35

(jw - 6) * (jl - 6) = 35

jw jl - 6 jl - 6 jw + 36 = 35

jw jl - 6 jl - 6 jw = 35 - 36

jw jl - 6 jl - 6 jw = -1



Now plug in jw from the top, and solve for jl

(143 / jl) jl - 6 jl - 6 (143 / jl) = -1

143 - 6 jl - (858 / jl) = -1

143 + 1 = 6 jl + (858 / jl)

144 = (6 jl^2 + 858) / jl

144 jl = 6 jl^2 + 858

6 jl^2 + 858 - 144 jl = 0

jl^2 - 24 jl + 143 = 0

jl^2 - 24 jl + 143 = 0

(jl - 13)(jl - 11) = 0



Two answers

jl - 13 = 0

jl = 13

And

jl - 11 = 0

jl = 11



So the dimentions of Jasmine's rectangle is 13 by 11, whci makes A the correct answer





Total distance = 8 * 7 = 56 miles

The time to qualify = 56 / 105.66 = 0.53 hours



Noah had already done 3 * 7 = 21 miles

And it has taken him 21 / 92 = 0.2283 hours



Distance remaining = 56 - 21 = 35 miles

Time remaining = 0.53 - 0.2283 = 0.3017 hours



To go 35 miles in 0.3017 hours, you have to go

35 / 0.3017 = 116 mph



So the correct answer is C



I hope this helped



Kia