Question

.
leind the area
of В
two side
triangle
of which are 17 cm and 12cm and its
perimeter us 54​

Answer 1

Correct Question:

Find the area of a triangle if the lengths of two sides of a triangle are 17 cm and 12 cm respectively and it's perimeter is 54.

Given:

✰ The length of two sides of a triangle are 17 cm and 12 cm respectively.

✰ Perimeter of triangle = 54 cm

To find:

✠ The area of triangle.

Solution:

❖ First we will find the third side of triangle by using formula to calculate perimeter because we already know that the perimeter of triangle is 54 cm and after finding the third side we will calculate semi perimeter and then the area of triangle using Heron's formula.

Let a, b, c be the lengths of sides of a given triangle, and 2s be the perimeter of triangle

Such that,

• a = 17 cm
• b = 12 cm
• 2s = 54 cm

✭ Perimeter of triangle = a + b + c ✭

➤ 54 = 17 + 12 + c

➤ 54 = 29 + c

➤ c = 54 - 29

➤ c = 25 cm

Now, let's calculate Semi-perimeter

⟹ Semi-perimeter = Perimeter/2

⟹ Semi-perimeter = 54/2

⟹ Semi-perimeter = 27 cm

Now,

✭ Area of triangle = √s ( s - a ) ( s - b ) ( s - c ) ✭

➤ Area of triangle = √27 ( 27 - 17 ) ( 27 - 12 ) ( 27 - 25 )

➤ Area of triangle = √27 ( 10 ) ( 15 ) ( 2 )

➤ Area of triangle = √27 × 10 × 15 × 2

➤ Area of triangle = √3 × 9 × 2 × 5 × 3 × 5 × 2

➤ Area of triangle = √3 × 3 × 3 × 2 × 5 × 3 × 5 × 2

➤ Area of triangle = √3 × 3 × 3 × 3 × 2 × 2 × 5 × 5

➤ Area of triangle = 3 × 3 × 2 × 5

➤ Area of triangle = 90 cm²

∴ The area of triangle = 90 cm²

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