Question

The perimeter of any triangle is 40 cm. If it's two sides are 8cm & 15 cm respectively, then find its area & also find the length of perpendicular, drawn from a vertex to the longest side​

Answer 1

Solution:

Given:

⇒ Perimeter of triangle = 40 cm

⇒ Two sides = 8 cm and 15 cm.

To Find:

⇒ Area of triangle

⇒ Length of perpendicular, drawn from a vertex to the longest side​.

Formula used:

$\sf{\implies Area=\sqrt{s(s-a)(s-b)(s-c)}\;\;\;\;[Heron's\;Formula]}$

$\sf{\implies Area\;of\;triangle=\dfrac{1}{2}\times B\times H}$

Two, side of triangle given in the question. Let 3rd side be x cm.

⇒ Perimeter = A + B + C

⇒ 40 = 8 + 15 + x

⇒ 40 = 23 + x

⇒ x = 40 - 23

⇒ x = 17 cm.

So, 3rd side be 17 cm.

⇒ s = (a + b + c)/2

⇒ s = (8 + 15 + 17)/2

⇒ s = 20 cm

Now, by Heron's Formula.

$\sf{\implies Area=\sqrt{s(s-a)(s-b)(s-c)}\;\;\;\;[Heron's\;Formula]}$

$\sf{\implies Area=\sqrt{20(20-8)(20-15)(20-17)}}$

$\sf{\implies \sqrt{20\times 12\times 5\times 3}}$

$\sf{\implies Area=\sqrt{3600}}$

$\sf{\implies Area = 60\;cm}$

Hence, Area of triangle is 60 cm.

Now,

$\sf{\implies Area\;of\;triangle=\dfrac{1}{2}\times B\times H}$

$\sf{\implies 60 = \dfrac{1}{2}\times 17 \times H}$

$\sf{\implies 120=17H}$

$\sf{\implies H = \dfrac{120}{17} = 7.05\;cm}$

Hence, length of perpendicular is 7.05 cm.

Answer 2

Answer:

Step-by-step explanation:

Given :-

Perimeter of any triangle = 40 cm

Two Sides of triangle = 8 cm and 15 cm

To Find :-

Area of Triangle and Height

Solution :-

Let the remaining side be x cm.

⇒ x + 8 + 15 = 40 cm

⇒ x + 23 = 40 cm

⇒ x = 40 - 23

⇒ x = 17 cm

= 15² + 8²

= 225 + 64

= 189 = 17²

This shows triangle is right angled.

Area of triangle = 1/2 × 8 × 15 = 60 cm ²

⇒ 1/2 × 17 × h = 60

⇒ h = 7.05 cm