Here is another Math Stumper...Remember to show your work!?

Question

A rectangular house which measures 20 m by 10 m has an electrical outlet at a corner of the house. An electric mower, connected by a cord to the outlet, can reach a maximum distance of 15 m. What is the largest area of lawn which can be cut?

What does * stand for?

Answer 1

You have to draw a picture.
Draw a rectangle with two of the sides twice the others. Make the long sides the vertical ones (that's the way I have them.)
Name the right hand lower corner C and the left hand lower corner L. Assume the outlet at C.
Okay, the electric cord can go up to 15 m along the right edge (above C) and swing in a circle (with C the center)all the way around until it is straight along the bottom of the house 5 m to the left of L.
So far this is 3/4 of the area of a circle of radius 15.
Now, continuing on the left side of the house, L acts as the center of a circle of 5 m. You get 1/4 of a circle of radius 5 on that side. Add the two areas.
If you need more help with this: [e-mail]

Answer 2

175 * Pi m^2

Rational:

The 15 m cord is tied to one corner of the house. Therefore, the cord's length allows the mower to cut an area that is 3/4 of a circle with a radius of 15 m

A = pi * r^2 * 3/4 = 675/4 * pi

On the 10 m long side of the house, the mower can still go 5 meters into the "back yard." This is a 1/4 circle of radius 5m.

A = pi * r^2 * 1/4 = 25/4 *pi

675/4 * pi + 25/4 * pi = 700/4 * pi = 175 * Pi m^2

Answer 3

Once you draw it out you see that all you need is the areas of 3/4 of a circle 15m radius and 1/4 of a circle of 5m radius.

1/4pi5^2 + 3/4pi15^2
= 549.78 m^2