Question

The sides of a triangle are 8cm, 15cm and 17cm. Find its perimeter and its area. Also find the length of the altitude drawn on the side with length 17cm.

Answer 1

Perimeter of triangle is 40 (cm). Area of triangle is 60$(cm^{2})$. Altitude on side 17 cm is 7.059 (cm).

Step-by-step explanation:

1. Side of triangle is 8 cm, 15 cm and 17 cm.

So  

Perimeter of triangle = Sum of side of triangle

Perimeter of triangle= 8+15+ 17=40 (cm)

2. If we see side of triangle

$8^{2}+15^{2}=17^{2}$

$64+225=17^{2}$

$289=17^{2}$

$17^{2}=17^{2}$

Means it satisfied Pythagoras rule

It must be a right angle triangle, and right angle opposite to side longest side 17 (cm).

3. Base =15 cm

   Perpendicular= 8 cm

   Hypotenuse =17 cm

4. So area of triangle $=\frac{1}{2}\times base\times perpendicular=\frac{1}{2}\times 15\times 8=60(cm^{2})$

5.

Area of triangle$=\frac{1}{2}\times base\times Perpendicular=\frac{1}{2}\times Hypotenuse\times altitude$

  We can also write

  $\frac{1}{2}\times Hypotenuse\times altitude=$ Area of triangle

  $\frac{1}{2}\times 17\times altitude= 60$

  On solving

  Altitude =7.059 (cm)

 

Answer 2

Side of triangle=8cm,15cm,17cm

So,

Perimeter of triangle=Sum of side of triangle

Perimeter of triangle=8cm+15cm+17cm

=40cm

If side of triangle

8²+15²=17²

64+225=17²

289=17²

17²=17²(means Pythagorean Rule)

It must be right angle triangle and right angle opposite to side longest side=17cm.

Base=15cm

Perpendicular=8cm

Hypotenuse=17cm

So,

Area of triangle=1/2*Base*Perpendicular

=1/2*15*8

=60cm²

Area of triangle=1/2*Base*Perpendicular=1/2*Hypotenuse*Altitude

So,

1/2*Hypotenuse*Altitude=Area of triangle

1/2*17*Altitude=60

Altitude=2/17*60

Altitude=7.05882353=7.059

Thus,

Altitude=7.059cm

Perimeter of triangle=40cm

Area of triangle=60cm