Question

Three sides of a triangle plot are 13 cm , 14cm and 15cm.Find the area of the plot.How much minimum distance has a man to walk if he wants to come to the longest side from the opposite corner?​

Answer 1

Answer:

• Area of the plot : 84cm²
• Shortest distance to reach the longest side from the opposite corner is 11.2cm

Explanation :

Given sides of the plot :

• 13cm, 14cm, and 15cm.

Area of the triangle is given by :

→ √s(s - a)(s - b)(s - c)

Where,

• a = 13cm.
• b = 14cm.
• c = 15cm.

Finding ‘s’ (Semi-perimeter)

→ s = (a + b + c) ÷ 2

→ s = (13 + 14 + 15) ÷ 2

→ s = 42 ÷ 2

→ s = 21cm.

Substitute the values :

→ √21(21 - 13) (21 - 14) (21 - 15)

→ √21(8) (7) (6)

→ √7,056

→ 84

The area of the plot is 84cm²

Now,

We need to find the shortest distance to reach its longest side i.e., 15cm (base) from its opposite corner. ( from point A to D )

Following the figure,

We have, base = 15cm

Shortest distance from point A to D is the height of the triangular plot.

So,

We can say that,

Area of the plot = ½ • base • height

Or

→ 84 = ½ • 15 • h

→ 84*2/15 = h

→ 11.2 = h

Hence, the required shortest distance is 11.2cm.

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