Question

the altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm find the area of the triangle​

Answer 1

ANSWER:-

Given:

The altitude drawn to the base of an Isosceles ∆ is 8cm & the perimeter is 32cm.

To find:

Find the area of the triangle.

Solution:

We know that, perimeter of ∆;

=) Side + Side + Side.

Therefore,

P= AB + BC + CA = 32

=) x + BC + x=32

=) 2x + BC =32

=) BC= 32 -2x

=) DC= 32-2x/2

=) DC= 16 -x

Therefore,

Using the Pythagoras Theorem;

AC² = AD² + DC²

=) x² = 8² + (16-x)²

=) x² = 64 + 256 + x² -32x

=) 64 +256 = 32x

=) 320 =32x

=) x= 320/32

=) x= 10

So,

BC = 32 - 2x

BC= 32 -2(10)

BC= 32 -20

BC= 12cm

Now,

Area of ∆.

$= > \frac{1}{2} \times \:BC \times AD\\ \\ = > \frac{1}{2} \times 6 \times 8 \\ \\ = > 3 \times 8 \\ \\ = > 24 {cm}^{2}$

Hence,

Area of triangle is 24cm².

Hope it helps ☺️

Answer 2

Answer:

the answers are in the above pictures