Answer:
[tex]\boxed {\tt 13.75 \ yards}[/tex]
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
where [tex]a[/tex] and [tex]b[/tex] are the legs and [tex]c[/tex] is the hypotenuse.
One of the legs is 10 yards, and the other is unknown. The hypotenuse is 17 yards, because it is the longest side.
[tex]a= 10 \ yd\\b=b\\c= 17 \ yd[/tex]
Substitute the values into the formula.
[tex](10 \ yd)^2+b^2=(17 \ yd)^2[/tex]
Evaluate the exponents.
- (10 yd)²= 10 yd * 10 yd = 100 yd²
[tex]100 \ yd^2+b^2= (17 \ yd)^2[/tex]
- (17 yd)²= 17 yd * 17 yd=289 yd²
[tex]100 \ yd^2+b^2= 289 \ yd^2[/tex]
Now, solve for b. First, subtract 100 yards squared from both sides of the equation.
[tex]100 \ yd^2-100 \ yd^2+b^2= 289 \ yd^2- 100 \ yd^2[/tex]
[tex]b^2=289\ yd^2-100 \ yd^2[/tex]
[tex]b^2=189 \ yd^2[/tex]
Finally, take the square root of each side of the equation.
[tex]\sqrt{b^2} =\sqrt{189\ yd^2}[/tex]
[tex]b=\sqrt{189 \ yd^2}[/tex]
[tex]b=13.7477271 \ yd[/tex]
Round to the nearest hundredth. The 7 in the thousandth place tells us to round the 4 to a 5.
[tex]b \approx 13.75 \ yd[/tex]
The other side of the garden is about 13.75 yards long.
