Question

if the sides of a triangle are 13 cm ,5cm and 12cm,then find the length of the altitude corresponding to the longest side as base by using heron's formula.
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Answer 1

Answer:

Step-by-step explanation:

Given :-

Sides of triangle = 13 cm, 5 cm and 12 cm

To Find :-

The longest side as base

Formula to be used :-

Area of triangle = √[s(s-a)(s-b)(s-c)]

Solution :-

Using Heron's Formula, we get

S = (a + b + c)/2

S = 5 + 12 + 13/2

S = 30/2

S = 15

Area of triangle = √[s(s - a)(s - b)(s - c)]

Area of triangle = √[15 (1 - 5) (15 - 12) (15 - 13)

Area of triangle = √[15 (10) (3) (2)

Area of triangle = √[ 900]

Area of triangle = √[30 × 30]

Area of triangle = 30 cm²

Now, we will find the attitude

Area of triangle = 1/2 × base × altitude

30 × 2  = 13 ×  altitude

60 / 13 = altitude

4.6 cm = altitude

Hence, the altitude corresponding to the longest side is 4.6 cm.

Answer 2

SOLUTION:-

Given:

·If the sides of a triangle are 13cm,5cm and 12cm.

To find:

The length of the altitude [height] corresponding to the longest side as base.

Explanation:

We have sides of a triangle are:

• First side, A=13cm
• Second side, B=5cm
• Third side, C=12cm

∴According to the question:

We can use Heron's Formula to determine the area of a triangle;

Therefore,

Semi-perimeter(S)⇒$\frac{a+b+c}{2}$

Or

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

Therefore,

Semi-perimeter(S)=$\frac{13cm+5cm+12cm}{2}$

Semi-perimeter(S)=$\frac{30cm}{2}$

Semi-perimeter(S)= 15cm

&

Area of Δ =$\sqrt{s(s-a)(s-b)(s-c)}$

Area of Δ= $\sqrt{15(15-13)(15-5)(15-12)}$

Area of Δ= $\sqrt{15(2)(10)(3)}$

Area of Δ= $\sqrt{3 *5*2*2*5*3}$

Area of Δ= (2×3×5)cm²

Area of Δ= 30cm².

Now,

• We can determine the height of a triangle using formula of the area of Δ.
• Area of Δ= 30cm²
• The longest side of a triangle is base.

Area of triangle ⇒$\frac{1}{2} *Base*Height$

$\frac{1}{2} *13cm*Height=30cm^{2} \\\\\frac{13}{2} *Height=30cm^{2} \\Height=(\frac{30*2}{13}) cm\\\\Height= \frac{60}{13}cm \\Height= 4.61cm$

Thus,

The altitude[height] of a triangle is 4.61cm.