To find the missing side lengths in right triangles, we use the
Pythagorean theorem:
>
a² + b² = c²
Where:
-
a and
b are the two shorter sides (legs) of the triangle.
-
c is the longest side (hypotenuse), opposite the right angle.
We’ll solve each problem one by one.
---
Problem 1:
Given: legs = 12 yd and x; hypotenuse = 15 yd
So:
x² + 12² = 15²
x² + 144 = 225
x² = 225 - 144 = 81
x = √81 =
9
✔ Answer:
9 yd
---
Problem 2:
Given: leg = 16 in, other leg = x; hypotenuse = 20 in
So:
x² + 16² = 20²
x² + 256 = 400
x² = 400 - 256 = 144
x = √144 =
12
✔ Answer:
12 in
---
Problem 3:
Given: legs = 5 ft and 12 ft; hypotenuse = x
So:
5² + 12² = x²
25 + 144 = x²
169 = x²
x = √169 =
13
✔ Answer:
13 ft
---
Problem 4:
Given: leg = 8 yd, other leg = x; hypotenuse = 10 yd
So:
x² + 8² = 10²
x² + 64 = 100
x² = 100 - 64 = 36
x = √36 =
6
✔ Answer:
6 yd
---
Problem 5:
Given: leg = 18 in, other leg = x; hypotenuse = 30 in
So:
x² + 18² = 30²
x² + 324 = 900
x² = 900 - 324 = 576
x = √576 =
24
✔ Answer:
24 in
---
Problem 6:
Given: legs = 36 ft and x; hypotenuse = 60 ft
So:
x² + 36² = 60²
x² + 1296 = 3600
x² = 3600 - 1296 = 2304
x = √2304 → Let’s check: 48 × 48 = (50 - 2)² = 2500 - 200 + 4 = 2304
✔
x =
48
✔ Answer:
48 ft
---
Final Answer:
1) 9 yd
2) 12 in
3) 13 ft
4) 6 yd
5) 24 in
6) 48 ft
Parent Tip: Review the logic above to help your child master the concept of right triangle pythagorean theorem worksheet.
