Solve the problem
-A $15 \mathrm {~cm}$ by $18 \mathrm {~cm}$ rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is $418 \mathrm {~cm} ^ { 2 }$ ?
A) $3 \mathrm {~cm}$
B) $1 \mathrm {~cm}$
C) $2 \mathrm {~cm}$
D) $3.5 \mathrm {~cm}$

Question

Quizplus · Accepted Answer

The width of the path can be found by setting up an equation for the total area. Let the width of the path be $x$ cm. The new dimensions of the garden including the path will be $(15 + 2x) $ cm by $(18 + 2x) $ cm. The total area is given by the equation $(15 + 2x)(18 + 2x) = 418$. Simplifying, we get $270 + 66x + 4x^2 = 418$, which simplifies further to $4x^2 + 66x - 148 = 0$. Solving this quadratic equation for $x$, we find $x = 2$ cm as the width of the path that satisfies the given conditions.

Solve the Problem -A 15 cm15 \mathrm {~cm}15 cm By 18 cm18 \mathrm {~cm}18 cm Rectangular Garden Is to Have a Gravel Path of Uniform

Solve the Problem
-A $15 \mathrm {~cm}$ By $18 \mathrm {~cm}$ Rectangular Garden Is to Have a Gravel Path of Uniform