Question

the length of sides of triangle are 9cm 12cm . 15cm find the length of altitude corrosponding to the s​

Answer 1

Step-by-step explanation:

Given length of the sides of triangle are 9 cm,12 cm and 15 cm

We know that median=

2

2b

2

+2c

2

−a

2

Here a=15 cm b=12 cm and c=9 cm

Then median of longest side=

2

2(12)

2

+2(9)

2

−(15)

2

=

2

288+162−22 ⇒=

2

225 = 2,/15 =7.5 cm

Answer 2

Correct question

$\:\:$

The length of sides of triangle are 9cm 12cm . 15cm find the length of altitude corresponding to the sides

$\:\:$

A n s w e r

$\:\:$

G i v e n

$\:\:$

• Length of first Side is 9cm

• Length of second side is 12 cm

• Length of third side is 15 cm

$\:\:$

F i n d

$\:\:$

• Length of altitude corresponding to the sides

$\:\:$

S o l u t i o n

$\:\:$

$\underline{ \underline{\bold{\texttt{Area of triangle :}}}}$

$\:\:$

➠ $\sf \sqrt { s(s - a)(s - b)(s - c) }$ ⚊⚊⚊⚊ ⓵

$\:\:$

Where ,

$\:\:$

• a = First side

• b = Second side

• c = Third side

• s = Semi perimeter

• $\sf s = \dfrac { a + b + c } { 2 }$

$\:\:$

$\underline{ \underline{\bold{\texttt{Area of the given triangle :}}}}$

$\:\:$

• a = 9 cm

• b = 12 cm

• c = 15 cm

• $\sf s = \dfrac { 9 + 12 + 15 } { 2 } = 18 cm$

$\:\:$

⟮ Putting the above values in ⓵ ⟯

$\:\:$

: ➜ $\sf \sqrt { s(s - a)(s - b)(s - c) }$

$\:\:$

: ➜ $\sf \sqrt { 18(18 - 9)(18 - 12 )(18 - 15) }$

$\:\:$

: ➜ $\sf \sqrt { 18(9)(6)(3) }$

$\:\:$

: ➜ $\sf \sqrt { 18(3)(3)(18) }$

$\:\:$

: ➜ 18 × 3

$\:\:$

: : ➨ 54 cm²

$\:\:$

• Hence the area of triangle is 54 cm²

$\:\:$

$\underline{ \underline{\bold{\texttt{Area of triangle :}}}}$

$\:\:$

➠ $\sf A = \dfrac { 1 } { 2 } \times b \times h$ ⚊⚊⚊⚊ ⓶

$\:\:$

Where ,

$\:\:$

• A = Area of triangle

• b = Base

• h = Perpendicular height = Altitude corresponding the base

$\:\:$

Case I [ With base as 9 cm ]

$\:\:$

Let altitude corresponding the 9 cm base be 'H1'

$\:\:$

• A = 54 cm²

• b = 9 cm

• h = H1

$\:\:$

⟮ Putting the above values in ⓶ ⟯

$\:\:$

: ➜ $\sf A = \dfrac { 1 } { 2 } \times b \times h$

$\:\:$

: ➜ $\sf 54 = \dfrac { 1 } { 2 } \times 9 \times H1$

$\:\:$

: ➜ $\sf H1 = \dfrac { 54 \times 2 } { 9 }$

$\:\:$

: : ➨ H1 = 12 cm

$\:\:$

• Hence altitude corresponding to side 9 cm is of length 12 cm

$\:\:$

Case II [ With base as 12 cm ]

$\:\:$

Let altitude corresponding the 12 cm base be 'H2'

$\:\:$

• A = 54 cm²

• b = 12 cm

• h = H2

$\:\:$

⟮ Putting the above values in ⓶ ⟯

$\:\:$

: ➜ $\sf A = \dfrac { 1 } { 2 } \times b \times h$

$\:\:$

: ➜ $\sf 54 = \dfrac { 1 } { 2 } \times 12 \times H2$

$\:\:$

: ➜ $\sf H2 = \dfrac { 54 \times 2 } { 12 }$

$\:\:$

: : ➨ H2 = 9 cm

$\:\:$

• Hence altitude corresponding to side 12 cm is of length 9 cm

$\:\:$

Case III [ With base as 15 cm ]

$\:\:$

Let altitude corresponding the 15 cm base be 'H3'

$\:\:$

• A = 54 cm²

• b = 15 cm

• h = H3

$\:\:$

⟮ Putting the above values in ⓶ ⟯

$\:\:$

: ➜ $\sf A = \dfrac { 1 } { 2 } \times b \times h$

$\:\:$

: ➜ $\sf 54 = \dfrac { 1 } { 2 } \times 15 \times H3$

$\:\:$

: ➜ $\sf H3 = \dfrac { 54 \times 2 } { 15 }$

$\:\:$

: : ➨ H3 = 7.2 cm

$\:\:$

• Hence altitude corresponding to side 15 cm is of length 7.2