Each side of the smaller square in the figure below is n inches long, and each side of the larger square is p inches longer than a side of the smaller square. the area of the larger square is how many square inches greater than the area of the smaller square?

2np + p²

Step-by-step explanation:

The general formula for the area of a square is A = s², where s = the length of one side of the square.  In the case of the smaller square the area would be: n x n = n².  Since the side of the larger square is 'p' inches longer, the length of one side is 'n + p'.  To find the area of the larger square, we have to take the length x length or (n +p)².

Using FOIL (forward, outside, inside, last):

(n + p)(n+p) = n² + 2np + p²

Since the area of the first triangle is n², we can subtract this amount from the area of the larger square to find out how many square inches greater the larger square area is.

n² + 2np + p² - n² = 2np + p²

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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step-by-step explanation: