Question

The perimeter of an isosceles triangle is 44cm and the ratio of the equal side to its base is 4:3. The area of the triangle is *
12√55 cm²
4√55 cm²
3√55 cm²
16√55 cm²​

Answer 1

AnsWer :-

• option A is correct

Solution :-

The perimeter of isosceles triangle is 44 cm.

Perimeter of isosceles triangle = 2× equal sides × base

Let the length of equal side be 4x and base 3x

Then,

➝ 2 × 4x + 3x = 44

➝ 8x + 3x = 44cm

➝ 11x = 44cm

➝ x = 44/11

➝ x = 4 cm

Now,

Length of equal side = 4x = 4×4 = 16 cm,

and

Length of base = 3x = 3×4 = 12 cm .

Now, we have to find the height of the triangle ,

So, using Pythagoras theorem in half of the triangle because Pythagoras theorem needs right angle triangle,

So, The base = 12/2 = 6cm

Pythagoras theorem :-

Hypotenuse² = base² - height ²

➜ 16² = 6² - height ²

➜ 256 - 36 = height ²

➜ Height ² = 220

➜ Height = √220

Now,

Area of triangle = 1/2 × base × height

→ 1/2 × 12 ×√220

→ 6×√220

→ 6 × 2√55

→ 12 √55

therefore , The area of triangle is 12√55 ,so , option A is correct

Answer 2

Area of traingle is 12√55 cm².

Option A is correct.

Given:

• The perimeter of an isosceles triangle is 44cm.
• The ratio of the equal side to its base is 4:3.

To find:

• The area of the triangle is:
• A) 12√55 cm²
• B) 4√55 cm²
• C) 3√55 cm²
• D) 16√55 cm²

Solution:

Formula to be used:

Heron's formula

$\boxed{\bf Ar(\triangle) = \sqrt{s(s - a)(s - b)(s - c)} }$

where, s is semiperimeter and a,b and c are the sides of traingle.

Step 1:

Find the sides of the triangle.

We know that,

In isosceles triangle 2 sides are equal.

The ratio of the equal side to its base is 4:3.

So,

$4x + 4x + 3x = 44$

$11x = 44$

$\bf x = 4$

Sides are 4×4, 4×4 and 3×4.

Thus,

Sides are 16, 16 and 12 cm.

Step 2:

Find the area of the triangle.

$s = \frac{44}{2}$

$\bf s = 22\:cm$

$Ar(\triangle) = \sqrt{22(22 - 16)(22 - 16)(22 - 12)}$

$Ar(\triangle) = \sqrt{22 \times 6 \times 6 \times 10}$

$Ar(\triangle) = \sqrt{11 \times 2 \times 6 \times 6 \times 5 \times 2}$

$Ar(\triangle) = \sqrt{ {2}^{2} \times {6}^{2} \times 55}$

$\bf Ar(\triangle) = 12 \sqrt{55} \: {cm}^{2}$

Thus,

Area of traingle is 12√55 cm².

Option A is correct.

Learn more:

1) Find the area of the triangle whose lengths of sides are 15m, 17m, 21m (use Heron’s Formula) and verify your answer by u...

https://brainly.in/question/5484018

2) Find the area of a right-angled triangle whose base is 3 cm and height is 4 cm.

https://brainly.in/question/21599570

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