We are given that we are making a kite and we want to evaluate the perimeter of a kite. Let's take a look at the given diagram.
Since diagonals of a kite are perpendicular, we can see that this kite is made of two pairs of congruent right triangles. Let's call the hypotenuses of these triangles x and y.
Now, using the Pythagorean Theorem, we can write equations to find the values of x and y.
lc x^2= 12^2+ 15^2 & (I) y^2= 12^2+20^2 & (II)
Let's solve the above equations. Notice that, since x and y represent the side lengths, we will consider only the positive cases when taking a square root of x^2 and y^2.
lcx^2=12^2+15^2 & (I) y^2=12^2+20^2 & (II)
(I), (II): Calculate power
lx^2=144+225 y^2=144+400
(I), (II): Add terms
lx^2=369 y^2=544
(I), (II): sqrt(LHS)=sqrt(RHS)
lsqrt(x^2)=sqrt(369) sqrt(y^2)=sqrt(544)
(I), (II): sqrt(a^2)=a
lx=sqrt(369) y=sqrt(544)
(I), (II): Calculate root
lx≈19.2 y≈23.3
Let's add this information to our diagram.
Finally, we will add all side lengths of this kite to evaluate its perimeter.
19.2+ 19.2+23.3+23.3=85
The perimeter of this kite is approximately 85 inches. Since we are given that the binding comes in packages of two yards, we need to convert inches to yards. Recall that we have 36 inches in each yard.
85in.*1yd/36in.≈ 2.36
Since each package has 2 yards of the binding and we need a little more than 2 yards for our kite we should buy 2 packages.
