To find the perimeter of a right-angled triangle with a base length of 20 cm and a height of 15 cm, follow these steps:
1. Identify the sides of the triangle:
- Base length ([tex]\( a \)[/tex]) = 20 cm
- Height length ([tex]\( b \)[/tex]) = 15 cm
- Hypotenuse ([tex]\( c \)[/tex]) is unknown.
2. Use the Pythagorean theorem to find the hypotenuse:
The Pythagorean theorem states that in a right-angled triangle: [tex]\(c = \sqrt{a^2 + b^2}\)[/tex].
For our triangle:
[tex]\[
c = \sqrt{(20)^2 + (15)^2}
\][/tex]
[tex]\[
c = \sqrt{400 + 225}
\][/tex]
[tex]\[
c = \sqrt{625}
\][/tex]
[tex]\[
c = 25 \text{ cm}
\][/tex]
3. Calculate the perimeter of the triangle:
The perimeter [tex]\( P \)[/tex] of a triangle is the sum of the lengths of its sides:
[tex]\[
P = a + b + c
\][/tex]
Substituting the values, we get:
[tex]\[
P = 20 \text{ cm} + 15 \text{ cm} + 25 \text{ cm}
\][/tex]
[tex]\[
P = 60 \text{ cm}
\][/tex]
So, the perimeter of the right-angled triangle with a base length of 20 cm and a height length of 15 cm is 60 cm.
