Question

Find the area of the triangle whose two sides are

of measures 13 cm and 14 cm and perimeter is

42 cm.​

Answer 1

$\huge \color{aqua}answer : -$

☆ 84 cm ²

$\huge\color{violet} explanation: -$

☆ To find :-

• The area of triangle

☆Given :-

• The measures of two sides of the triangle are 13 cm and 14 cm .

• The perimeter of triangle is 42 cm.

☆Assuming:-

• Let the other side of the triangle be x.

☆Solution:-

ATQ

13+14+x=42

=>27+x=42

=>x=42 -27

=> x= 15

☆Formula:-

• Area of scalene triangle

$- > \sqrt{s(s - a)(s - b)(s - c)}$

• Now the value of s :

$- >s = \frac{1}{2} (a + b + c)$

☆ The area :-

$s = \frac{1}{2} (13 + 14 + 15) \\ = >s = \frac{42}{2} = 21$

• Therefore, area of the triangle:

$\sqrt{21(21 - 13)(21 - 14)(21 - 15)} \\ = > \sqrt{21 \times 8 \times 7 \times 6} \\ = > \sqrt{7 \times 3 \times 2 \times 2 \times 2 \times 7 \times 3 \times 2} \\ = > 7 \times 3 \times 2 \times 2 = 21 \times 4 = 84 {cm}^{2}$

☆ Hence:

• Area of the triangle is 84 cm².

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Extra information:

• Area of triangle = 1/2 × base × height
• Pythagoras formula : Hypotenuse ²

--> Base²+height ²

• The sum of all Interior angles of triangle is 180°.

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hope it helps...... :)