Question

please write correctly with step by step please​

Answer 1

Ist part answer is 8 units

Answer 2

Answer:-

• Area = 8 cm².

• Length of Perpendicula from Anto BC = $\bf 2\sqrt{2}\:cm.$

Explanation:-

Given:-

• A trianlge ABC (See the Figure in attachment).

• $\tt\angle A = 90\degree.$

• AB = AC = 4 cm.

To Find:-

• The area of triangle.

• Length of perpendicular from A to BC.

Formula Used:-

1. Area of triangle,

$\\ \bf \longrightarrow A= \dfrac{1}{2} \times b \times h.$

Where,

• b = Base.
• h = Height.

2. Pythagoras theorem,

$\\ \tt\longrightarrow H {}^{2} = P {}^{2} + B {}^{2} .$

Where,

• A = Area.
• H = Hypotenuse.
• P = Perpendicular i.e height = h.
• B = Base = b.

So Here,

• B = AB = AC = P = 4 cm.

• H = ??.

• Let the length of perpendicular be AD.

Now,

By using formula (1) Area of triangle,

$\\ \tt = \dfrac{1}{ \cancel2} \times \cancel4 \: cm \times 4 \: cm.$

$\\ \tt = 2 \: cm \times 4 \: cm.$

$\\ \large\red{ \boxed{ \blue{ \bf = 8 \: cm {}^{2} .}}}$

Therefore Area of triangle is 8 cm².

And,

By using formula (2) we get:-

$\\ \tt\mapsto {H}^{2} = (4 \: cm) {}^{2} + (4 \: cm) {}^{2} .$

$\\ \tt\mapsto {H}^{2} = 16\: cm {}^{2} + 16 \: cm {}^{2} .$

$\\ \tt\mapsto {H}^{2} = 32 \: cm {}^{2} .$

$\\ \tt\mapsto H = \sqrt{32 \: cm {}^{2} }$

$\\ \bf \mapsto H = 4\sqrt{2} \: cm =BC.$

Also, As Since AD is perpendicular to hypotenuse so BD = CD .

$\\ \tt\mapsto CD = \dfrac{BC}{2}.$

$\\ \tt\mapsto CD = \frac{4 \sqrt{2} }{2} \: cm .$

$\\ \bf\mapsto CD = 2 \sqrt{2} \: cm.$

Also,

Since AD is Perpendicular to BC so <ADC = 90°.

And By applying pythagoras theorem we get:-

$\\ \tt\mapsto CD {}^{2} + AD {}^{2} = AC {}^{2}.$

$\\ \tt\mapsto(2 \sqrt{2} \: cm) {}^{2} + AD {}^{2} = (4 \: cm) {}^{2}$

$\\ \tt\mapsto AD {}^{2} = (4 \: cm) {}^{2} - (2 \sqrt{2} \: cm) {}^{2} .$

$\\ \tt\mapsto AD {}^{2} = 16 \: cm {}^{2} - 8 \: cm {}^{2} .$

$\\ \tt\mapsto AD {}^{2} = 8 \: cm {}^{2} .$

$\\ \tt\mapsto AD = \sqrt{8 \: cm {}^{2} } .$

$\\ \large \red{\mapsto \boxed{ \blue{ \bf AD = 2 \sqrt{2} \: cm.}}}$

Therefore Distance Of perpendicular from A to BC = $\bf 2\sqrt{2}$ cm.