Question

4. The unequal side of an isosceles triangle is 48 cm, and its perimeter is 108 cm. Find the area of the triangle.​

Answer 1

Answer:

Area of the isoceles is 432cm²

Explanation:

Given, the unequal side of an isoceles is 48cm.

It's perimeter is 108cm.

Let's calculate the two equal sides

Assuming the each of the equal sides as x

We know,

Perimeter of an isoceles triangle = 2a + b

Where, a denotes the each equal sides b is the unequal side.

So,

= 2(x) + b

But, the perimeter is 48cm (given)

According to the question,

⇒ 2x + 48 = 108

⇒ 2x = 108 - 48

⇒ 2x = 60

⇒ x = 60/2

⇒ x = 30

∴ Each equal sides measures 30cm.

Now,

Calculating it's area :-

Area of an isoceles is given by,

→ ½ × bh

Where, b is the base and h denotes the height of the triangle.

We have, b = 48cm

Calculating h :-

Lets draw a perpendicular bisector on the base from the top vertex as shown in the figure.

Now, the triangle is divided into two equal parts and forms two right angle triangle.

Applying Pythagoras theorem,

⇒ (h)² = (b)² + (p)²

Where,

• h(hypotenuse) = 30cm.
• b(base) = 24cm.
• p denotes the perpendicular.

Substituting the values,

⇒ (30)² = (24)² + (p)²

⇒ 900 = 576 + p²

⇒ 900 - 576 = p²

⇒ 324 = p²

⇒ √324 = p

⇒ 18 = p

∴ The perpendicular is 18cm.

So, the area of the traingle is :-

→ ½ × bh

→ ½ × 48*18

→ 48*9

→ 432cm²

∴ Area of the isoceles traingle is 432cm²