Question

The base of an isosceles triangle is 8 m more than its altitude.If the area is 192 m²,find the length of its sides

Answer 1

Step-by-step explanation:

there are 2 types of sets in this triangle

either root over 52 are equal or 12

Answer 2

Solution:

Given Data:  

The base of an isosceles triangle = 8 m

Area = 192$\mathrm{m}^{2}$

To Find:

To Calculate the length of its sides

Step-by-Step Explanation:

Step 1:

Area of the isosceles triangle$=\frac{1}{2} \times \text { base } \times \text { height }$

 $=\frac{1}{2} \times(8+x) \times(x)$

Step 2:

   $=\frac{1}{2} \times 8 x \times x^{2}$

   $=4 x+x^{2}$…………. (1)

Step 3: Area of isosceles triangle =192 cm

Step 4:

$x^{2}+4 x=192$

$x^{2}+4 x-192=0$

Step 5:

Using Quadratic equation:

$\mathrm{X}=6 \pm \sqrt{\frac{16-0}{2 a}}$

a=1 b=4 c=0

Step 6:

$\mathrm{x}=-\mathrm{b} \pm \frac{16-0}{2 a}$

$\mathrm{X}=-4 \pm \sqrt{\frac{16-0}{2 \times 1}}$

Step 7:

Result:

$\mathrm{x}=-4 \pm \sqrt{\frac{16-0}{2}}$

$\mathrm{x}=4 \pm \sqrt{\frac{16-0}{2}}$