Question

Given: ∆ABC, AB = BC, m∠1<90° Perimeter of ∆ABC = 25 Difference between two sides is 4 Find: AB, BC, AC

Answer 1

The value of is AB = BC =
`(29)/(3)` unit , AC is
`(17)/(3)` unit .

Explanation:

Given as :

In a triangle ABC ,

Let The three sides be AB , BC , CA

Side AB = Side BC , ∠B = 90°

Perimeter of ΔABC =25 unit

Or, AB + BC + CA = 25 unit

Or, AB + AB + CA = 25 unit

i.e 2 AB + CA = 25 unit .....1

And Difference between two sides = 4

So, AB - CA = 4 unit .......2

Now, According to question

From eq 1 and eq 2

(2 AB + CA) + (AB - CA) = 25 unit + 4 unit

Or, (2 AB + AB) + (CA - CA) = 29

Or, 3 AB + 0 = 29

∴ AB =
`(29)/(3)` unit

∵ BC = AB

So, BC =
`(29)/(3)` unit

Again

∵ AB - CA = 4 unit

So, AC = AB - 4

Or, AC =
`(29)/(3)` unit - 4 unit

Or, AC =
`(29 - 12)/(3)` unit

i.e AC =
`(17)/(3)` unit

So, The value AB = BC =
`(29)/(3)` unit , AC =
`(17)/(3)` unit

Hence, The value of is AB = BC =
`(29)/(3)` unit , AC is
`(17)/(3)` unit . Answer