We are given that Janice built a as shown below, and we're asked to evaluate its . To do this, we need to find all side lengths of this figure. Recall that in a consecutive sides are congruent. We will name the shorter sides x and the longer sides y.
Notice that in kites diagonals are to each other. Therefore, this figure has two pairs of .
To find the values of
x and
y, we can use the . Let's recall this theorem.
In a right triangle, the sum of the squaresof the lengths of the legs is equalto the square of the length of the hypotenuse.
a2+b2=c2
Using this theorem, we can create equations to find the missing side lengths. We can start with
x.
Let's write and solve an equation for
x. Notice that since
x represents the side length, we will consider only the positive case when taking a square root of
x2.
The length of the shorter sides are
10 inches. Next we will find the value of
y in the same way.
Let's write and solve an equation for
y. Again, notice that since
y represents the side length, we will consider only the positive case when taking a square root of
y2.
The length of the longer sides are
17 inches.
Finally, we will evaluate the perimeter by adding all side lengths.
P=10+10+17+17=54
The perimeter of the kite is
54 inches.
