Question

Mary crocheted a rectangular blanket whose diagonal measures approximately 7.21 feet. What are the most likely length and width measurements of the blanket ? Select the two correct answers.

Answer 1

If both sides are integers, one side will be 4 feet and the other will be 6 feet. The other solution is the symmetrical solution (4 feet instead of 6 feet, and 6 feet instead of 4 feet).

Explanation:

We have a rectangular blanket, that has a diagonal that measures h=7.21 feet.

The two sides of the rectangle a and b can be related to the diagonal h by the Pithagorean theorem:

`a^2+b^2=h^2`

Then, we can express one side in function of the other as:

`a^2+b^2=h^2\\\\a^2=h^2-b^2\\\\a=√(h^2-b^2)=√(7.21-b^2)=√(52-b^2)`

Then, if we define b, we get the value of a that satisfies the equation.

A graph of values of a and b is attached.

If both side a and b are integers, we can see in the graph that are only two solutions: (b=4, a=6) and (a=4, b=6).