Suppose a=3x b=4x.

Then according to Pythagorean theorem

(3x)^2+(4x)^2= 10^2

= = & gt9x^2+ 16x^2= 100

= = & gt25x^2= 100

= = & gtx=2

So a=3x=6.

b=4x=8

(2) Xiaoli walked north from home 15 meters, and then walked east for 25 meters. How many meters is Xiaoli from home at this time?

According to Pythagorean theorem

At this time, Xiaoli's distance from home = root number (15 2+25 2) = root number 850.

(3) The length of one right side of a right triangle is 12, and the lengths of the other two sides are natural numbers. Find all possible boundaries.

Suppose the other right angle has a side length of a and a hypotenuse length of b.

According to Pythagorean theorem

A2+12 2 = B2, because ab is a natural number.

Corresponding to 3 2+4 2 = 5 2

Maybe a b is

5 and 13 9 and 15 16 and 25.

Then the circumference may be 5+ 12+ 13=30 or 9+ 12+ 15=36 or 16+ 12+25=53.

(4) It is known that in △ABC, AB= 17cm, BC= 16cm, and the median line of BC =15cm. What triangle is it? And explain why.

Because the square of AB is equal to the square of AD plus the square of BD (BD is half of BC), the triangle ABD is a right triangle. So AD is the height of side BC of triangle ABC.

According to the meaning of the question, AD is the center line of BC, so DC=BD, angle ADB and angle ADC are right angles, so triangle ADC is a right triangle, and the square of AC is equal to the square of AD plus the square of CD, that is, AC is equal to AB, and this triangle is an isosceles triangle.

(5) Among the four ratios formed by line segment abc, the one that can form a right triangle is: (c)

A 2:3:4 B 3:4:6 C 5: 12: 13 D 4:6:7.

Only when C satisfies Pythagorean theorem 5 2+12 2 =13 2 can a right triangle be formed.