Question

I need help! please help anyone?!

What are the values of a and b?

Answer 1

a. a=9/2, b=15/2
b. a=15/2, b=9/2
c. a=16/3, b=15/2
d. a=9/2, b=13/2

Answer 2

from big triangle,
b^2+10^2=(a+8)^2
from small triangle,
a^2+6^2=b^2
so comparing value of b^2 we get,
a^2+6^2+10^2=a^2+16a+64
=>136-64=16a
=>72/16=a
=>a=9/2
so, b=sqrt(a^2+6^2)=sqrt(81/4+36)=sqrt(225/4)=15/2
now you find your answer

Answer 3

Theorem: If the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the lengths of the segments of the hypotenuse.

So, 8 is to 6 as 6 is to a.


8/6 = 6/a

8a = 36

a = 4.5 -->

Answer 4

Theorem: If an altitude is drawn to the hypotenuse of a right triangle, either leg of the triangle is the geometric mean between the length of the hypotenuse and the segment of the hypotenuse adjacent to that leg.

The hypotenuse is (4.5 + 8) = 12.5
The segment adjacent to the leg with length b = 4.5.

4.5 is to b as b is to 12.5

4.5/b = b/12.5

b^2 = (4.5)*(12.5)

Solve for the positive square root of b.
@dragontales