HomeWorking Mothersextra credit for math?
Posted in Working Mothers on 3rd October 2012

extra credit for math?
Judy and her daughter, Jen, like to spend quality time
together in their backyard garden, which is in the form of a
large rectangle. As they both like mathematics, they often
challenge each other by posing problems while they work.

One day Jen said to her mother, “Mom, I’ve just figured out
that I can save 20 meters by walking diagonally across the
garden rather than by walking around two adjacent sides.

Can you tell me the dimensions of the garden?” Judy
replied, “Honey, that’s not a fair question. Lots of
rectangles could work for that. I need some more
information.”

“Sorry, mother dear,” said Jen, with a twinkle in her eye.

“Okay then, the width is 25 meters.”

“Well now, that’s more like it,” answered Judy.

Then, scribbling a few numbers in the dirt (reminiscent of
another great mathematician), she quickly obtained the
missing dimension.

What is the missing dimension?

Show work please!
Thank you so much for the answer! I get it, but I’m still confused on how once you get the Pythagorean theorem equation and you substitute the one variable, how to simplify it down right. I tried, and I got it wrong :/
thank you soo much! Yes, I get it now 🙂 I never learned the FOIL technique, so I guess that’s why I had problems. Thank you again, I appreciate it!

Best answer(s):

Answer by Art Vandelay
Alright, the answer is 60 meters, and here’s how to do it:

You set up two equations with two unknowns.

Let’s call the length of the unknown side ‘x’ and the length of the diagonal ‘z’.

1st equation:

We know that z is 20 meters less than x + 25, so

z=x+25-20, so

z=x+5

2nd equation:

Pythagorean theorem
x^2 + 25^2 = z^2

Now, with these two equations, substitute (x-5) in for z in the second equation. Simplify to get

x=60 meters.

Good luck. Add details if you’re still confused.

————————————————
Edit: let me elaborate for you:

We substitute (x+5) for z into x^2 + 25^2 = z^2:

so, x^2 + 25^2 = (x+5)^2

Do you know how to expand the right side with the FOIL technique?:

we get x^2 + 625 = (x^2 + 10x + 25)

subtract x^2 from both sides…..

625 = 10x + 25

subtract 25 from both sides….

600 = 10x.

Divide by 10:

60 = x.

Clear now?

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