Question

4. The perimeter of a triangular field is 240m. Its two sides are 78 m and 50 m. Find the length of the altitude on the side of 50 m length from its opposite vertex,​

Answer 1

$\large\bf\underline{Given:-}$

• Perimeter of triangular field = 240m
• Length of two sides = 78m and 50m

$\large\bf\underline {To \: find:-}$

• length of the altitude on the side of 50 m length from its opposite vertex,

$\huge\bf\underline{Solution:-}$

Perimeter of triangular Field = 240m

Perimeter of triangle = sum of all sides.

Let the third side be x

➝ 240 = 78 + 50 + x

➝ 240 = 128 + x

➝ 240 - 128 = x

➝ 112 = x

So, the third side is 112m

Area of triangle by Heron's Formula:-

$\bf \large \: \sqrt{s(s - a)(s - b)(s - c)}$

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

• a = 50
• b = 78
• c = 112

$\rm \longmapsto \: s = \frac{50 + 78+ 112}{2} \\ \\ \rm \longmapsto \: s = \cancel\frac{240}{2} \\ \\ \rm \longmapsto \: s =120$

Area of triangular field :-

$\rm \longmapsto \: \sqrt{120(120 - 50)(120 - 78)(120 - 112)} \\ \\ \rm \longmapsto \: \sqrt{120 \times 70 \times 42 \times 8} \\ \\ \rm \longmapsto \: \sqrt{ 2,822,400} \\ \\ \bf \longmapsto \:1680 \: {m}^{2}$

$\bf \: area \: of \: triangle = \frac{1}{2} \times base \times height$

Let the height be h m

Area of triangle = 1/2 × 50 × h

➝ 1680 = 25h

➝ h = 1680/25

➝ h = 67.2

So, the length of altitude is 67.2m

Answer 2

Step-by-step explanation:

answer

answer

answer

using formula