We are interested in the dimensions of a certain rectangle. This rectangle has length 5 units more than the side of this square and width half the side of this square. If the two areas are equal, what are the rectangle's dimensions (w x h)?

Question

anonymous · Answer

lets say the side of the square is A units in length. Can you tell me what the length and width of the rectangle are, based on the side of the square?

anonymous · Answer

huh

anonymous · Answer

okay. let's try again. suppose the square has side of length A.

anonymous · Answer

k

anonymous · Answer

what does the question say the length of the rectangle is?

anonymous · Answer

it doesnt say but they have equal areas

anonymous · Answer

it does say. read the question properly.

anonymous · Answer

5 more than the side of the square?

anonymous · Answer

yes, very good. so if the side of the square is A, what is the length of the rectangle?

anonymous · Answer

a+5

anonymous · Answer

very good, in the same way, what is the width of the rectangle?

anonymous · Answer

a/2?

anonymous · Answer

excellent! you are on fire! now, what is the area of a square of side a?

anonymous · Answer

(a+5)(a/2)?

anonymous · Answer

that is the area of the rectangle. what is the area of the square?

anonymous · Answer

a squared

anonymous · Answer

okay very good! now, what does the question say about the area of the square and the rectangle?

anonymous · Answer

they're the same

anonymous · Answer

excellent, so what does that mean in terms of an equation?

anonymous · Answer

the answer is 10X5/2

anonymous · Answer

area of square = area of rectangle.

but we know that area of square = a squared.
and area of rectangle = (a+5)(a/2)