Question

In a scalene triangle,one side exceeds the other two side by 4 cm and 5 cm respectively and the perimeter of the triangle is 36 cm.find the are of the triangle? ​

Answer 1

Answer:

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Answer 2

Given - Perimeter

Find - Area

Solution - The area of the triangle is 12✓21 centimetres².

Let the two sides of the triangle be x and y. The other side of the triangle will be (x+4) or (y+5).

Find the value of x through the perimeter of the triangle.

x + x + 4 + y = 36

2x + y = 32 Equation 1

and x + y + 5 + y = 36

2y + x = 31 Equation 2

Multiplying equation 2 with 2

4y + 2x = 62 Equation 3

Subtracting Equation 1 from equation 3.

On subtraction we get -

3y = 30

y = 10 centimetres

So, the value of x -

x = 31 - 2*10

x = 31 - 20

x = 11 centimetres

The third side of the triangle will be = 11 + 4

The third side of the triangle = 15 centimetres

Hence, the sides of the triangle are 10, 11 and 15 centimetres.

Now find the area of the triangle.

Area = ✓s(s-a)(s-b)(s-c)

Further s will be calculated as -

s = a+b+c/2

s = 10 + 11 + 15/2

s = 18 centimetres

Keep the values in the formula to find the value of the area.

Area = ✓18 (18 - 10) (18 - 11) (18 - 15)

Area = ✓18*8*7*3

Area = ✓3*3*2*2*2*2*7*3

Area = 3*2*2✓7*3

Area = 12✓21 centimetres

So, the area of the given triangle is 12✓21 centimetres².