Hi someone please help me I'm not sure how to do thi If the longer base of triangle XYZ is three times the length of the shorter base, a, what is the length of the hypotenuse in terms of the shorter base?

The length of the hypotenuse is √(10)*a

Step-by-step explanation:

Remember the Pythagorean theorem.

If b is the larger base, and a the shorter base, and H is the hypotenuse:

a^2 + b^2 = H^2

now, we know that b = 3*a.

(3*a)^2 + a^2 = H^2

10*a^2 = H^2

√(10)*a = H

Then we have the length of the hypotenuse in terms of the shorter base, B.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.