Question

Two equal sides of an isosceles triangle are 4m less than 3 times the third side.Find the dimensions of the triangle, if the perimeter is 55m.​

Answer 1

GIVEN :-

in an isosceles ∆,

two equal sides are 4m less than three times the third side.

let the third side of the triangle be x.

therefore it's 1st and 2nd side are 3x - 4 each.

given the perimeter of the triangle = 55m

we know that, sum of all three sides of a triangle = perimeter of the triangle

➡ (3x - 4) + (3x - 4) + x = 55m

➡ 3x - 4 + 3x - 4 + x = 55m

➡ 7x - 8 = 55m

➡ 7x = 55 + 8

➡ 7x = 63

➡ x = 63/7

➡ x = 9

hence, the sides if the triangle are :-

» 1st and 2nd = (3x - 4)

= (3 × 9) - 4

= 27 - 4

= 23m

» 3rd side = x

= 9m

VERIFICATION :-

= 23 + 23 + 9

= 46 + 9

= 55m

hence verified!