Question

The length of an altitude from the vertex of a right angle in a triangle having legs 6 and 8 is ___ units
1. 10
2. 6
3. 4√3
4. 4√5
5. 5
Other: ???

Answer 1

Answer:

root36+64

root 100

10=>ANSWER

MARK AS "BRAINIEST" ANSWER.

Step-by-step explanation:

Answer 2

✰Answer✰

☛Given:

• It is an right angled triangle.
• Legs of triangle are 6 and 8.

☛To find:

• Altitude drawn from right angle to the hypotenuse.

✰Solution✰

♦️This question is completely based on visualization, So for Reference, Pls check the attachment.

We know that,

$\large{ \boxed{ \sf{ \green{area \: of \: triangle = \frac{1}{2} \times base \times corresponding \: altitude}}}}$

☛Here, In Triangle ABC, let the base is 6 cm.

Then corresponding height( on which it stands) would be 8cm.

☛Area of triangle ABC

$\large{ \sf{ \rightarrow \: \frac{1}{2} \times \: AB \times BC }} \\ \\ \large{ \sf{ \rightarrow \: \frac{1}{2} \times 8 \times 6}} \: {cm}^{2} \\ \\ \large{ \sf{ \rightarrow \: \frac{48}{2} }} \: \: {cm}^{2} \\ \\ \large{ \sf{ \rightarrow \: \boxed{ \purple{24 \: cm {}^{2} }}}}$

☛Now considering AC as base,

☛By using Pythagoras theoram,

$\large{ \sf{ \rightarrow \: AB {}^{2} + BC {}^{2} = AC {}^{2} }} \\ \\ \large{ \sf{ \rightarrow \: {8}^{2} + {6}^{2} = AC {}^{2} }} \\ \\ \large{ \sf{ \rightarrow \: 100 \: {cm}^{2} = {AC}^{2} }} \\ \\ \large{ \sf{ \rightarrow \: \boxed{ \purple{ AC = \: 10 \: cm}}}}$

☛So, now we have Base AC = 10 cm, We know that Area of triangle is 1/2 × base × corresponding height.

So, when Base is AC, Corresponding height= BD

☛Area will not change as it is the same triangle.

That means,

$\large{ \sf{ \rightarrow \: \frac{1}{2} \times BD \times AC = \frac{1}{2} \times AB \times BC}} \\ \\ \large{ \sf{ \rightarrow \: \frac{1}{2} \times BD \times 10 \: cm = 24 \: {cm}^{2} }} \\ \\ \large{ \sf{ \rightarrow \: BD = \frac{24 \times 2} {10} \: cm}} \\ \\ \large{ \sf{ \rightarrow \boxed{ \purple{\: BD = 4.8 \: cm}}}}$

✰So final Answer✰

$\large{ \therefore{ \boxed{ \green{ \sf{corresponding \: altitude \: from \: base \: AC = 4.8cm}}}}}$

♦️Other....