$2$-inch squares are cut from the corners of a $10$-inch square. What is the area of the largest square that fits the remaining space?

You'll want something like this:

enter image description here

i.e. where the side of the inscribed square goes through the corner points of the little cut out squares.

Draw some helpful little lines:

enter image description here

And you find that the area is the middle $6\times 6$ square plus exactly half of the area of all the black and blue triangles (since for every blue triangle there is a corresponding black triangle). So, the area is:

$$36 + \frac{4 \cdot 2 \cdot 6}{2}=36+24=60$$

Here's a graphical assist from @Blue:

enter image description here


The blue part has a total area of $2\times 2\times 6 = 24$, Thus, the largest area that can still fit is

$$10^2 - 4\times 2^2 - 24 = 60$$enter image description here

Tags:

Geometry

Area

Related

Associative Lie algebra Showing $\int_0^{\infty } \frac{1}{e^{2 x}+2 e^x \cos (x)+1} \, dx=\frac{\log (2)}{2}-\pi \sum _{n=0}^{\infty } \frac{1}{e^{\pi (2 n+1)}+1}$ $\sqrt{6}-\sqrt{2}-\sqrt{3}$ is irrational Solving equation for wifi password. If $A$ is $4\times2$ and $B$ is $2\times4$, prove that $AB$ is not invertible Logarithmic equation, some variables in bases and in arguments How can I prove mathematically the reflection matrix has only the eigenvalues 1 or -1? If two functions are mirror images of each other about the line $y=x$, are they inverses of each other? Prove that $\left ( 1+\frac{n^{\frac{1}{n}}}{n} \right )^\frac{1}{n}+\left ( 1-\frac{n^{\frac{1}{n}}}{n} \right )^\frac{1}{n}<2$ What even *are* elliptic functions? Master Theorem: $T(n) = 3T(\frac{n}{3} − 2) + \frac{n}{2}$ Is mapping generators to generators, and then extending, a well-defined homomorphism?

Recent Posts