To find the hypotenuse of a right triangle, we use the Pythagorean theorem:
a² + b² = c², where
c is the hypotenuse (the side opposite the right angle), and
a and
b are the other two sides.
We’ll solve each problem one by one.
---
1) Triangle ABC:
AB = 15 yd, BC = 8 yd → Find AC (hypotenuse)
AC² = AB² + BC²
AC² = 15² + 8² = 225 + 64 = 289
AC = √289 =
17 yd
✔ Check: 15-8-17 is a known Pythagorean triple. Correct.
---
2) Triangle XYZ:
YZ = 5 ft, XZ = 12 ft → Find XY (hypotenuse)
XY² = YZ² + XZ²
XY² = 5² + 12² = 25 + 144 = 169
XY = √169 =
13 ft
✔ Check: 5-12-13 is a known Pythagorean triple. Correct.
---
3) Triangle EFG:
EF = 4 in, FG = 3 in → Find EG (hypotenuse)
EG² = EF² + FG²
EG² = 4² + 3² = 16 + 9 = 25
EG = √25 =
5 in
✔ Check: 3-4-5 is a classic Pythagorean triple. Correct.
---
4) Triangle PQR:
PQ = 20 yd, PR = 21 yd → Find QR (hypotenuse)
QR² = PQ² + PR²
QR² = 20² + 21² = 400 + 441 = 841
QR = √841 =
29 yd
✔ Check: 20-21-29 — let’s verify: 20²=400, 21²=441, sum=841, √841=29. Correct.
---
5) Triangle TUV:
TU = 36 ft, UV = 48 ft → Find TV (hypotenuse)
TV² = TU² + UV²
TV² = 36² + 48² = 1296 + 2304 = 3600
TV = √3600 =
60 ft
✔ Check: 36-48-60 → divide by 12 → 3-4-5 triple. So 12×5=60. Correct.
---
6) Triangle LMN:
NM = 24 ft, LM = 10 ft → Find LN (hypotenuse)
LN² = NM² + LM²
LN² = 24² + 10² = 576 + 100 = 676
LN = √676 =
26 ft
✔ Check: 10-24-26 → divide by 2 → 5-12-13 triple. So 2×13=26. Correct.
---
Final Answer:
1) AC = 17 yd
2) XY = 13 ft
3) EG = 5 in
4) QR = 29 yd
5) TV = 60 ft
6) LN = 26 ft
Parent Tip: Review the logic above to help your child master the concept of easy pythagorean theorem worksheet printable.
