Question

select the correct answer
a basket weaver is making a square basket. a sketch of the top shows the its diagonal will measure 6 inches. what is the perimeter of the top of the basket to the nearest inch?
a. 20 in
b. 34 in
c. 17 in
d. 24 in

Explanation:

Step1: Use Pythagorean theorem for square

Let side - length of square be $a$. In a square, if the diagonal is $d$, by Pythagorean theorem $d^{2}=a^{2}+a^{2}=2a^{2}$. Given $d = 6$ inches, so $6^{2}=2a^{2}$, which is $36 = 2a^{2}$.

Step2: Solve for side - length $a$

Divide both sides of $36 = 2a^{2}$ by 2: $\frac{36}{2}=a^{2}$, so $a^{2}=18$. Then $a=\sqrt{18}=3\sqrt{2}$ inches.

Step3: Calculate the perimeter $P$ of the square

The perimeter of a square is $P = 4a$. Substitute $a = 3\sqrt{2}$ into the formula: $P=4\times3\sqrt{2}=12\sqrt{2}\approx12\times1.414 = 16.968\approx17$ inches.

Answer:

C. 17 in