Math, asked by neyunkim, 1 year ago

Using Heron's formula find the area of a right triangle in which the sides containing the right angle measures 20 cm and 15 ​

Answers

Answered by manas3379
28

Step-by-step explanation:

It is given that the right angle is formed by the sides measuring 20 cm and 15 cm.

Therefore, let perpendicular = 20cm

Base = 15 cm

Using Pythagoras Therom,

Perpendicular² + Base² = Hypotenuse ²

(20)² + (15)² = Hypotenuse ²

Hypotenuse² = 625

Hypotenuse = 25 cm

Thus, we now know the third side, Hypotenuse = 25.

Semi perimeter = (15 + 20 + 25)/2

= 30 cm

Using Heron's formula,

Area = √[30(30 - 15)(30 - 20)(30 - 25)]

= √[30 × 15 × 10 × 5]

= √[2×3×5 × 3×5 × 2×5 × 5]

= 2 × 3 × 5²

= 150cm²

Thus, area = 150cm²

Hope it helps!

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Answered by Anonymous
46

\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}

Assumption

∆PQR (Right angled triangle)

PQ = c = 20cm

QR = a = 15cm

{\boxed{\sf\:{Using\;Pythagoras\;Theorem}}}

PR = √{(PQ)² + (QR)²}

PR = √{(20)² + (15)²}

PR = √(400 + 225)

PR = √625

PR = 25 cm

Also here,

\tt{\rightarrow s=\dfrac{a+b+c}{2}}

\tt{\rightarrow s=\dfrac{15+25+20}{2}}

\tt{\rightarrow s=\dfrac{60}{2}}

s = 30 cm

{\boxed{\sf\:{Using\;Herons\;Formula :-}}}

\tt{\rightarrow\sqrt{s(s-a)(s-b)(s-c)}}

\tt{\rightarrow\sqrt{30(30-15)(30-25)(30-20)}}

\tt{\rightarrow\sqrt{30\times 15\times 5\times 10}}

\tt{\rightarrow\sqrt{15\times 2\times 5\times 3\times 5\times 5\times 2}}

= 15 × 2 × 5 cm²

= 150 cm²

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