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The base of an isosceles triangle is 12 ...

The base of an isosceles triangle is `12 cm` and its area is `48` `"cm"^(2)`. Find the equal sides of the triangle.

A

`"14 cm"`

B

`"10 cm"`

C

`"8 cm"`

D

`"12 cm"`

Text Solution

Verified by Experts

The correct Answer is:
B
Let length of equal sides be `x cm.`
`:.` `a=x cm, b=x cm` and `c=12 cm`
`s=(a+b+c)/(2)=(x+x+12)/(2)`
`= ((2x+12)/(2))` cm
`= (x+6)` cm
Area of triangle `=sqrt(s(s-a)(s-b)(s-c))`
`48=sqrt((x+6)(x+6-x)(x+6-x)(x+6-12))`
`48=sqrt((x+6)xx6xx6xx(x-6))`
`48=sqrt((x^(2)-36)xx36)`
Squaring both sides,
` 48xx48=(x^(2)-36)xx36`
` rArr " " x^(2)-36=(48xx48)/(36)`
`rArr " " x^(2)-36=64`
`rArr " " x^(2)=100`
or `" " x=+- 10`
Side of a triangle cannot be negative.
So, `" "` `x=10`
Hence, length of equal sides are `10 cm` each.
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