Find the value of x using the diagram below. round to the nearest whole number. picture attached.

Both triangles are right triangles. x is the hypotenuse of the upper one. ThePythagorean formula  will give the value of x. One side is known, The other side we will find using the fact that the lower right triangle is isosceles. The hypotenuse of an isosceles right triangle has a length of times the length of one of the legs. In this case 14. So the hypotenuse of the lower triangle is also the short side of the upper triangle. Using Pythagoras





 

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

The answer is e &