# The side of a triangle are in the ratio 3:4:5 and its perimeter is 84.find the lenght of its sides

by lovingumann 24.02.2016

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by lovingumann 24.02.2016

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A 3:4:5 triangle is a right triangle. How can you be sure? Assume that the sides are actually 3 cm, 4 cm, and 5 cm. Apply the Pythagorean theorem which says that in a right triangle the sum of the squares of the two small sides - called the legs - will equal the square of the longest side - called the hypotenuse. In this case, that would mean:

.

.

And when you square the terms the result is:

.

.

This is a true statement because the left side of this equation does equal the right side. Therefore, a triangle having sides whose ratios are 3:4:5 is a right triangle.

.

Again, let's assume that we have a 3:4:5 triangle that has sides actually 3 cm, 4 cm, and 5 cm in length. That means its perimeter would be:

.

cm

.

But the problem says that you have a triangle with a perimeter of 144 cm. Therefore, the given triangle has a perimeter that is 12 times greater than the perimeter of the 3 cm, 4 cm, 5 cm triangle we assumed. So we multiply all the sides of our assumed triangle by 12 and we get:

.

.

To have sides in the ratio of 3:4:5 and a perimeter of 144 cm, the sides must be 36 cm, 48 cm, and 60 cm. (Note ).

.

Now we can calculate the area of the given triangle. Since we determined that this triangle was a right triangle, we know that the two legs (the 36 cm and the 48 cm sides) are perpendicular to each other. That being the case we can say that one of the legs is the base of the triangle and the other is the perpendicular height. The area of a triangle is computed from the relationship:

.

.

in which A is the area, b is the length of the base, and h is the dimension of the height. So for this problem we can substitute the dimensions of the two legs and write the equation as:

.

.

If you multiply out the right side of this equation you find that:

.

.

That's the answer for the area, and don't forget to add that the units are square centimeters or for short.

.

Hope this explanation helps you to understand the problem a little better.

.

.

And when you square the terms the result is:

.

.

This is a true statement because the left side of this equation does equal the right side. Therefore, a triangle having sides whose ratios are 3:4:5 is a right triangle.

.

Again, let's assume that we have a 3:4:5 triangle that has sides actually 3 cm, 4 cm, and 5 cm in length. That means its perimeter would be:

.

cm

.

But the problem says that you have a triangle with a perimeter of 144 cm. Therefore, the given triangle has a perimeter that is 12 times greater than the perimeter of the 3 cm, 4 cm, 5 cm triangle we assumed. So we multiply all the sides of our assumed triangle by 12 and we get:

.

.

To have sides in the ratio of 3:4:5 and a perimeter of 144 cm, the sides must be 36 cm, 48 cm, and 60 cm. (Note ).

.

Now we can calculate the area of the given triangle. Since we determined that this triangle was a right triangle, we know that the two legs (the 36 cm and the 48 cm sides) are perpendicular to each other. That being the case we can say that one of the legs is the base of the triangle and the other is the perpendicular height. The area of a triangle is computed from the relationship:

.

.

in which A is the area, b is the length of the base, and h is the dimension of the height. So for this problem we can substitute the dimensions of the two legs and write the equation as:

.

.

If you multiply out the right side of this equation you find that:

.

.

That's the answer for the area, and don't forget to add that the units are square centimeters or for short.

.

Hope this explanation helps you to understand the problem a little better.

HENCE THE ANGLE ARE

3x, 4x, 5x

Hence the equation is

3x+4x+5x = 84

12x = 84

x = 84/12 = 7

The angle are:-

3*7 = 21

4*7 = 28

5*7 = 35

The length of side are 21, 35, 28