Given: A right triangle in which an altitude is drawn from the right angle vertex to the hypotenuse.

To find: 'x' the larger leg of triangle

Solution,

Using let rule for similarity in right triangle:

$\frac{leg}{part} = \frac{hypotenuse}{leg} \\ or \: \frac{x}{27} = \frac{3 + 27}{x} \\ or \: x \times x = 27(3 + 27) \\ or \: x \times x = 81 + 729 \\ or \: {x}^{2} = 810 \\ or \: {x}^{2} = 81 \times 10 \\ or \: {x} = \sqrt{81 \times 10} \\ or \: x = \sqrt{81} \times \sqrt{10} \\ or \: x = \sqrt{ {(9)}^{2} } \times \sqrt{10} \\ \: x = 9 \sqrt{10}$

Hope this helps...

Good luck on your assignment..

7 0

3 years ago

Help me with the question in the pic

Nonamiya [84]

Answer:

208

Step-by-step explanation:

With shapes like these, it's easier to break it into two squares. Area is width times height, and you know the taller square has a width of 6 and height of 16, so the area of that would be 96.

For the other square, subtract the 6 from the 14 to get the width, 8. For the height, subtract the 2 from the 16, and you get 14. 14x8 is 112.

Now add the two areas together, and you get 208.

3 0

2 years ago

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