Question

the varners live on a corner lot. often, children cut across their lot to save walking distance. the diagram to the right represents the corner lot. the childrens path is represented by a dashed line. approximate the walking distance that is saved by cutting across their property instead of walking around the lot. the walking distance that is saved by cutting across the lot is (round the final answer to the nearest integer as needed. round to the nearest thousandth as needed.) cubic feet feet square feet

Explanation:

Step1: Apply Pythagorean theorem

$x^2 + (x+12)^2 = 50^2$
Expand: $x^2 + x^2 +24x +144 =2500$
Simplify: $2x^2 +24x -2356=0$ → $x^2 +12x -1178=0$

Step2: Solve quadratic equation

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$a=1,b=12,c=-1178$
Discriminant: $12^2 -4(1)(-1178)=144+4712=4856$
$\sqrt{4856}\approx69.69$
$x=\frac{-12+69.69}{2}\approx28.845$ (positive root)

Step3: Calculate saved distance

Path around: $x+(x+12)=2x+12\approx2(28.845)+12=70.69$
Saved: $70.69 -50\approx21$

Answer:

21 feet