Question

The sides of a triangle are 16 cm, 12 cm and 20cm. Find area of the triangle and height of the triangle,corresponding to the largest side​

Answer 1

Step-by-step explanation:

To find the area of triangle we need to find the height of the triangle.

This can be done by using pythogoras theorem..

AB^2=AC^2+BC^2

256=AC^2+100

AC=√156=12.4(approx)

Area of triangle =1/2×base×height

=1/2×20×12.4

= 124cm^2.

Answer 2

ANSWER:-

Given:

The sides of a ∆ are 16cm,12cm &20cm.

So,

Let A,B, &C are the sides of a ∆ and s is the semi-perimeter, then its given;

⚫A (16cm)

⚫B (12cm)

⚫C (20cm)

Using Heron's Formula:

$s = \frac{A + B + C}{2} \\ \\ = > \frac{16 + 12 + 20}{2} \\ \\ = > \frac{48}{2} \\ \\ = > 24cm$

Now,

Area of triangle:

$A = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = > \sqrt{24(24 - 16)(24 - 12)(24 - 20)} \\ \\ = > \sqrt{24(8)(12)(4)} \\ \\ = > \sqrt{2 \times 2 \times 2 \times 3 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 2 \times 2} \\ \\ = > 2 \times 2 \times 2 \times 2 \times 2 \times 3 \\ \\ = > 96 {cm}^{2}$

Therefore,

⚫Longest side, C= 20cm.

⚫Corresponding to this side as base, the altitude will be;

$= > A = \frac{1}{2} \times b \times h \\ \\ = > 96 = \frac{1}{2} \times 20 \times h \\ \\ = > 96 = 10 \times h \\ \\ = > h = \frac{96}{10} \\ \\ = > h = 9.6cm$

Hope it helps ☺️