Question

Find the sides of a triangle if two of its sides are equal, the third side is 1 1 3 cm longer than the others, and its perimeter is 5 2 5 cm.

Answer 1

Answer:
`137(1)/(3)\ cm,\ 137(1)/(3)\ cm,\ 250(1)/(3)\ cm`

Explanation:

Let x be the equal sides of the triangle .

The , the third side would be x+113 cm.

The perimeter is the sum of all sides of a triangle.

So , The perimeter of triangle would be x+x+(x+113)= 3x+113 --------(1)

Since , it is given that the perimeter of triangle is 525. -----(2)

So from (1) and (2) , we have

`3x+113=525\\\\ 3x=525-113=412\\\\ x=(412)/(3)=137(1)/(3)`

Then, third side =
`137(1)/(3)+113=250(1)/(3)\ cm`

Hence , the sides of a triangle are:
`137(1)/(3)\ cm,\ 137(1)/(3)\ cm,\ 250(1)/(3)\ cm`

Answer 2

Answer: 1 16/45, 1 16/45, 2 31/45

Explanation:

Say x is the equal side of the triangle.

The third side would be x+113 cm.

The perimeter is the sum of all sides of a triangle.

So, the perimeter of the triangle would be x+x+(x+113)= 3x+113

Since the triangle's perimeter is 5 2/5, 3x + 1 1/3 = 5 2/5.

1 1/3 is 1 5/15. 5 2/5 is 5 6/15. 5 6/15 - 1 5/15 = 4 1/15.

This means 3x = 4 1/15.

4 1/15 = 61/15

3x = 61/15

To make 3x into x, you can multiply it by 1/3.

3x*1/3 is x. 61/15*1/3 = 61/45.

x = 1 16/45 because 61/45 = 1 16/45.

The longer side is x + 1 1/3 so you have to add 1 1/3 to 1 16/45 which is

2 31/45.

So, the sides are 1 16/45, 1 16/45 and 2 31,45.