Question

لا
HI
4. The lengths of the sides of a triangle
are in the ratio 3:4:5 and its
perimeter is 60
cm. Find its area​

Answer 1

Step-by-step explanation:

I Hope it Help you ...............

Answer 2

Answer:

The area of a triangle is 150cm².

Step-by-step explanation:

Consider the provided information.

Here in this question it is provided that the lengths of the sides of a triangle are in the ratio 3:4:5 and the perimeter of a triangle is 60cm.

And, we exigency to find out the area of a triangle.

Let us assume that, the sides of a triangle is 3x, 4x and 5x respectively.

We know that,

Perimeter of triangle = sum of all sides.

Substituting all the given sides in the formula, we get:

$\longrightarrow 3x + 4x + 5x = 60$

$\longrightarrow 7x + 5x = 60$

$\longrightarrow 12x = 60$

$\longrightarrow x = \dfrac{60}{12}$

$\longrightarrow x = 5$

Therefore,

• 3x = 3 × 5 = 15cm
• 4x = 4 × 5 = 20cm
• 5x = 5 × 5 = 25cm.

Now,

We have three sides of a triangle, so first we need to find the semi-perimeter of triangle.

We know that,

Semi-perimete = Perimeter/2.

Substituting the given values in the formula, we get:

$= \dfrac{60}{2}$

$= 30$

Finally,

We will find the area of triangle.

We know that,

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

This formula is known as heron's formula.

Substituting all the given sides in the formula, we get:

$= \sqrt{30(30 - 15)(30 - 20)(30 - 20)}$

$= \sqrt{30 \times 15 \times 10 \times 5}$

$= \sqrt{450 \times 10 \times 5}$

$= \sqrt{4500 \times 5}$

$= \sqrt{22500}$

$= 150$

Hence, the area of a triangle is 150cm².

#Learn more:

If the sides that form the right angle of a triangle are 3.5 cm and 4.2 cm long, find the area of the triangle.

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