Question

7. In triangle ABC,
AB = AC = x; BC = 10 cm and the area of
the triangle is 60 cm^2.Find x.

Answer 1

area of triangle =1/2 lb

60 = 1/2 × 10x

120 = 10x

x = 120/10.  

x = 12

Answer 2

Answer →

Value of x is 13 cm .

Solution→

Given =

• Area of ∆ ABC = 60cm²
• Side AB = AC = x cm
• BC = 10 cm .

Now calculating area of given ∆ using herons formula

Herons formula = $\huge\sqrt{s(s-a)(s-b)(s-c)}$

Here, s ( semi Perimeter) = $\huge\frac{X+X+10}{2}$

S = x +5

Area =

$60 = \sqrt{x + 5(x + 5 - x)(x + 5 - x)(x + 5 - 10)}$

$60 = \sqrt{25(x + 5)(x - 5)}$

Squaring both sides

3600 = 25 ( x +5) ( x-5)

3600 = 25 (x²-5²)

3600 = 25x²-625

4225 = 25x²

$\frac{4225}{25} = {x}^{2}$

169 = x²

+/-(13) = x

But as we know that side cannot be -ve so x will be 13 cm