Question

11. Find the area of triangle two sides of which are 8 cm and 11 cm and the
perimeter is 32 cm.​

Answer 1

Given:-

• Two sides of the triangle are 8cm and 11cm.

• Perimeter of the triangle is 32cm.

To Find:-

• Find the area of the triangle.

Concept:-

• Let's go through the concept first. Concepts used here is Area of a traingle(Heron's Formula).Heron's Formula gives the area of a triangle when the length of all three sides are known.Unlike other triangle area formulae,there is no need to calculate angles or other distances in the triangle first.

• Substitute the given values in the equation and find the area of it.Let's do it.

Formulae Applied:-

• Area of a triangle = √[S(s - a)(s - b)(s - c)]

Solution:-

Length of the first side (a) is 8cm.

Length of the second side (b) is 11cm.

Length of third side (c) be x.

Perimeter of the triangle is 32cm.

Firstly, we should find the Semiperimeter

Semiperimeter(S) = perimeter/2

⟹ perimeter/2

⟹ 32/2

⟹ 16

Hence,

Semiperimeter of the triangle is 16cm.

Now,we should find the unknown side x(c).

Perimeter of a Triangle = a + b + c(Sum of all sides)

⟹ a + b + c = 32

⟹ 8 + 11 + x = 32

⟹ 19 + x = 32.

⟹ x = 32 - 19

⟹ x = 13

⟹ x = 13

Hence,

The length of third side (c) is 13cm.

═════════════════════════

According to the question we have!

Area of a triangle = √[S(s - a)(s - b)(s - c)]

⟹ √[S(s - a)(s - b)(s - c)]

⟹ √[16(16 - 8) × (16 - 11) × (16 - 13)]

⟹ √[16 × (8) × (5) × (3)]

⟹ √[(8 × 2) × 8 × 5 × )]

⟹ √[(8 × 8) × (2 × 5 × 3)]

⟹ √8^2 × √30

⟹ 8 × √30

⟹ 8√30

⟹ 8√30cm^2

Hence,

The area of the triangle is 8√30cm^2.

═════════════════════════

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Answer 2

Answer:

Given:-

Two sides of the triangle are 8cm and 11cm.

Perimeter of the triangle is 32cm.

To Find:-

Find the area of the triangle.

Concept:-

Let's go through the concept first. Concepts used here is Area of a traingle(Heron's Formula).Heron's Formula gives the area of a triangle when the length of all three sides are known.Unlike other triangle area formulae,there is no need to calculate angles or other distances in the triangle first.

Substitute the given values in the equation and find the area of it.Let's do it.

Formulae Applied:-

Area of a triangle = √[S(s - a)(s - b)(s - c)]

Solution:-

Length of the first side (a) is 8cm.

Length of the second side (b) is 11cm.

Length of third side (c) be x.

Perimeter of the triangle is 32cm.

Firstly, we should find the Semiperimeter

Semiperimeter(S) = perimeter/2

⟹ perimeter/2

⟹ 32/2

⟹ 16

Hence,

Semiperimeter of the triangle is 16cm.

Now,we should find the unknown side x(c).

Perimeter of a Triangle = a + b + c(Sum of all sides)

⟹ a + b + c = 32

⟹ 8 + 11 + x = 32

⟹ 19 + x = 32.

⟹ x = 32 - 19

⟹ x = 13

⟹ x = 13

Hence,

The length of third side (c) is 13cm.

═════════════════════════

According to the question we have!

Area of a triangle = √[S(s - a)(s - b)(s - c)]

⟹ √[S(s - a)(s - b)(s - c)]

⟹ √[16(16 - 8) × (16 - 11) × (16 - 13)]

⟹ √[16 × (8) × (5) × (3)]

⟹ √[(8 × 2) × 8 × 5 × )]

⟹ √[(8 × 8) × (2 × 5 × 3)]

⟹ √8^2 × √30

⟹ 8 × √30

⟹ 8√30

⟹ 8√30cm^2

Hence,

The area of the triangle is 8√30cm^2.