Daniela needs to cut a rectangular hole in a wall where a new window will be installed. the window will be 4 feet high and 3 feet wide. she draws the outline for the window on the wall. if the only measurement tool that she has is a measuring tape, how can she be sure the shape she drew is a rectangle?

Measure the diagonals, they should be 5 feet (3,4,5 triangle).

Step-by-step explanation:

As a more general answer, the diagonal measurements of ANY rectangle will be equal. You can calculate the correct measurement using A^2 + B^2 = C^2. A and B are the lengths of the sides and C is the length of the diagonals.

, and

for

step-by-step explanation:

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

note the following:

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