Question

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

Answer 1

Answer:

x = 13 cm

Step-by-step explanation:

As per the question,

In triangle ABC,

AB = AC = x

BC = 10 cm

Area = 60 cm²

By Heron’s formula,

$Area\ of\ triangle\ =\sqrt{s(s-a)(s-b)(s-c)}$

Where,

$s=\frac{a+b+c}{2}$

Now,

In triangle ABC

$s=\frac{x+x+10}{2}$

s = x + 5

Therefore,

$Area\ of\ triangle\ =\sqrt{(x+5)(x+5-x)(x+5-x)(x+5-10)}$

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

3600 = 25(x² - 25)

x² = 169

After solving this, we get

x = 13 cm

Hence, the required value of x = 13 cm