Question

The perimeter of an isosceles triangle is 24cm. The length of its congruent sides is 13cm less than twice the length of its base. Find the lengths of all sides of the triangle.

Answer 1

lengths of the sides of isoceles triangles are 7,7,10

Answer 2

Let the sides be x, y, z

Let the 2 congruent sides be x and z

According to above situation:-

x + y + z = 24cm....(1)

x =z = 2y- 13 cm....(2)

By substituting x=z in (1)

2z + y = 24cm

z=2y - 13cm

z -2y + 13=0....(3)

2z + y - 24= 0....(4)

BY USING ELIMINATION METHOD...

2z + y - 24=0 *(1)

z - 2y +13 =0 *(2)

2z+ y - 24=0

-(2z - 4y + 26=0)

2z + y - 24=0

-2z +4y -26 =0

= 0+5y-50=0

5y = 50

y= 50/5

y=10 cm...(5)

By substituting (5) in (3)

z -2y + 13 =0

z-20 +13 =0

z - 7 =0

z= 7cm

AS x = z

x = z =7 cm

y= 10 cm

VERIFICATION :-

Substituting all the values in (1)

x + y + z =24

7 + 7 + 10 = 24

14 +10 = 24

24=24

SO THERE IS YOUR ANSWER

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