Let’s solve this step by step.
We are told the
perimeter of the kite is 86 ft.
A kite has two pairs of adjacent sides that are equal. Looking at the diagram:
- The top two sides are both labeled
3y → so they’re equal (as expected in a kite).
- The bottom two sides are both labeled
6y - 2 → also equal.
- The horizontal diagonal is split into two parts:
5x - 15 and
2x + 3. But note — these are *not* sides of the kite! They are parts of the diagonal inside the kite. So we do
not add them to the perimeter.
✔ Perimeter = sum of all four outer sides.
So:
Perimeter = 3y + 3y + (6y - 2) + (6y - 2)
Let’s simplify that:
= 6y + 12y - 4
= 18y - 4
We’re told the perimeter is 86 ft, so:
18y - 4 = 86
Now solve for y:
Add 4 to both sides:
18y = 90
Divide both sides by 18:
y = 5
Wait — but the question asks for
x, not y!
Look again at the diagram. The horizontal diagonal is made of two segments:
5x - 15 and
2x + 3. In a kite, one diagonal is bisected (cut in half) by the other. Since the vertical diagonal is drawn with a right angle symbol and appears to be the axis of symmetry, it likely bisects the horizontal diagonal.
That means the two halves of the horizontal diagonal should be equal:
→
5x - 15 = 2x + 3
Now solve for x:
Subtract 2x from both sides:
3x - 15 = 3
Add 15 to both sides:
3x = 18
Divide by 3:
x = 6
✔ Let’s double-check:
If x = 6,
Left part: 5(6) - 15 = 30 - 15 = 15
Right part: 2(6) + 3 = 12 + 3 = 15 → Equal! Good.
And just to make sure everything fits:
We found y = 5 earlier.
Top sides: 3y = 15 each → total 30
Bottom sides: 6y - 2 = 30 - 2 = 28 each → total 56
Total perimeter: 30 + 56 = 86 → matches!
Everything checks out.
Final Answer:
6
Parent Tip: Review the logic above to help your child master the concept of kites and trapezoids worksheet.
