We are given 8 problems involving right triangles (and one rectangle), and we must use the
Pythagorean Theorem:
> In a right triangle, if `a` and `b` are the legs, and `c` is the hypotenuse, then:
>
a² + b² = c²
Let’s solve each problem step by step.
---
Problem 1
Legs: 8 and 6 → find hypotenuse `c`
Equation:
8² + 6² = c²
64 + 36 = c²
100 = c²
c = √100 =
10.0
✔ Answer: 10.0
---
Problem 2
One leg = `a`, other leg = 24, hypotenuse = 26
Equation:
a² + 24² = 26²
a² + 576 = 676
a² = 676 - 576 = 100
a = √100 =
10.0
✔ Answer: 10.0
---
Problem 3
One leg = 5, hypotenuse = 13, find other leg `b`
Equation:
5² + b² = 13²
25 + b² = 169
b² = 169 - 25 = 144
b = √144 =
12.0
✔ Answer: 12.0
---
Problem 4
One leg = `a`, other leg = 11, hypotenuse = √137
Equation:
a² + 11² = (√137)²
a² + 121 = 137
a² = 137 - 121 = 16
a = √16 =
4.0
✔ Answer: 4.0
---
Problem 5
Legs: 3 and 4 → find hypotenuse `x`
Equation:
3² + 4² = x²
9 + 16 = x²
25 = x²
x = √25 =
5.0
✔ Answer: 5.0
---
Problem 6
This is a right triangle with hypotenuse = 10, one leg = 6, find other leg `x`
Equation:
x² + 6² = 10²
x² + 36 = 100
x² = 64
x = √64 =
8.0
✔ Answer: 8.0
---
Problem 7
This is a
rectangle with width = 12, diagonal = 15, find height `x`
In a rectangle, the diagonal forms a right triangle with length and width.
Equation:
x² + 12² = 15²
x² + 144 = 225
x² = 225 - 144 = 81
x = √81 =
9.0
✔ Answer: 9.0
---
Problem 8
This is a
trapezoid, but we can drop a perpendicular from the top right corner to the base to form a right triangle.
- The horizontal leg of the triangle = total base (10) minus top (3) =
7
- The vertical leg = height =
6
- We need to find the slanted side `x` (hypotenuse)
Equation:
x² = 7² + 6²
x² = 49 + 36 = 85
x = √85 ≈
9.2195...
Rounded to nearest tenth →
9.2
✔ Answer: 9.2
---
##
✔ Final Answers:
1.
10.0
2.
10.0
3.
12.0
4.
4.0
5.
5.0
6.
8.0
7.
9.0
8.
9.2
All answers rounded to the nearest tenth as instructed.
Parent Tip: Review the logic above to help your child master the concept of solving pythagorean theorem worksheet.
