Question

Find the area of a triangle whose sides 34 cm, 20 cm and 42 cm. Hence, find the length of the altitude corresponding to the shortest side.

Answer 1

Answer:

h=33.6 cm

Step-by-step explanation:

area=336 cm2

area=1/2 bh

336=1/2 x 20 x h

h=33.6cm

Answer 2

Question -:

Find the area of a triangle whose sides 34 cm, 20 cm and 42 cm. Hence, find the length of the altitude corresponding to the shortest side.

Explanation -:

Given :

• Sides of a triangle = 34cm, 20cm and 42cm

Need to find :

• Area of the triangle.
• Length of the altitude corresponding to the shortest side.

Solution -:

We will use Heron's formula to find the area of the triangle

$\star \: \small\boxed{ \rm{ Area \: of \: a \: triangle = \sqrt{s(s - a)(s - b)(s - c)} }}$

Where,

• a = 34 cm, b = 20 cm and c = 42 cm

$\small\bf{ The \: value \: of \: s =\dfrac{a + b + c}{2}}$

Substituting the values of a = 34 cm, b = 20 cm and c = 42 cm.

$\small\sf {The \: value \: of \: s = \dfrac{34 + 20 + 42}{2} = 48}$

Substituting the values of a,b,c and s in the above formula

$\small\sf { Area \: of \: a \: triangle = \sqrt{48(48 - 34)(48 - 20)(48 - 42)} }$

$\small\rm{Area \: of \: a \: triangle = \sqrt{48 \times 14 \times 28 \times 6} }$

$\small\rm{Area \: of \: a \: triangle = \sqrt{6 \times 4 \times 2 \times 7 \times 2 \times 4 \times 7 \times 6} }$

$\small\rm{ Area \: of \: a \: triangle =6 \times 7 \times 4 \times 2 = 336 }$

Area of a triangle = 336 cm².

Calculating altitude to the shortest side

The shortest side of a triangle is 20 cm

Area of a triangle = 336 cm².

$\star \: \small\boxed{ \rm{Area \: of \: a \: triangle = \frac{1}{2} × base × height}}$

$\small\sf{ 336 = \dfrac{1}{2} × 20 × h}$

$\small\sf{336 \times 2 = 20h}$

$\small\sf{672 = 20h}$

$\small\sf{ \cancel\dfrac{672}{20} = h}$

$\small\bf{h = 33.6 \: cm}$

Final Answer -

• Area of the triangle is 336 cm².
• Length of the altitude to the shortest side is 33.6 cm.

$\rule{185mm}{4pt}$