Question

an isosceles triangle, the difference between one of the equal sides and the unequal side (longest of the three) is 3/10 of the sum of the equal sides. If the perimeter of the triangle is 90 cm, then find the length of unequal side in centimetres.

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Answer 1

Answer:

Let equal sides of isosceles triangle=x

So their sum=x+x=2x

3/10of 2x=3x/5

Difference of one equal and one unequal side=3x/5

Let unequal side =y

x-y=3x/5

5(x-y)=3x

5x-5y=3x

5x-5y-3x=0

2x-5y=0

Perimeter of triangle =x+x+y=90

2x+y=90

2x+y-90=0

Two equations are 2x-5y=0. Eq1

2x+y-90=0. Eq2

Subtracting eq1-eq2

2x-5y+0-(2x+y-90)=0

2x-5y+0-2x-y+90=0

-6y+90=0

-6y=-90

y=15

Hence the length of unequal side=15