Question 4

Geometry Level 2

A rectangular frame measuring $10"$ by $15"$ has five square holes for photos. Four of the holes are $2"$ by $2",$ and one hole is $3"$ by $3".$ The portion of the frame's area that was not cut away for photo holes can be expressed as $\frac{A}{B}$ for positive coprime $A$ and $B.$ Find $A+B.$

The answer is 11.

1 solution

Trevor B.
May 25, 2014

The total area of the frame is $150\text{ in}^2$ The area of the cut away holes is $4\times(2\times2)+3\times3=16+9=25\text{ in}^2.$ The area of the frame that was not cut away is $150-25=125\text{ in}^2.$ The fraction of the area not cut away is $\dfrac{125\text{ in}^2}{150\text{ in}^2}=\dfrac{5}{6}.$ Thus, $A=5$ and $B=6,$ so $A+B=\boxed{11}$

"Portion that was not cut away" could be interpreted as the area that was not cut away and as the fraction of the original area that was not cut away.

Guiseppi Butel - 7 years ago

yes. By "portion" i understand area not a fraction.Ah this language err gonna cost me pts.

Chandrachur Banerjee - 7 years ago

i did a very stupid mistake mistakenly!!!

Parth Lohomi - 6 years, 11 months ago

Question 4

The answer is 11.

1 solution

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