Question

This user "venus1234" removed my question for no reason. However, I'm going to ask again.

Sarah has a rectangular sheet of paper. Its shorter side is 23 cm long.

She cuts it in half and makes two identical rectangles that are similar to
the original sheet of paper.

Calculate the longer side length of the original sheet of paper.
Give your answer to 3 s.f.

Answer 1

Answer:

$32.5 cm$

Step-by-step explanation:

Since the rectangles are similar the ratio between the longer side and the shorter side will always be the same

We can call a the longer side and b the shorter side of the original rectangle so we make a ratio

$\frac{a}{b}$

Now im assuming Sarah cut the paper in the way of the longer side so since length a was cut in half we can represent it as

$\frac{a}{2}$

And b will stay the same but now since a was cut in half we can assume that b is the longer side now so we put it on top of the ratio

$\frac{b}{\frac{a}{2} }$

Now we set the 2 ratios equal to each other

$\frac{a}{b} =\frac{b}{\frac{a}{2} }$

We know the value of b(the shorter side) is 23 as stated in the question so we can fill that in

$\frac{a}{23} =\frac{23}{\frac{a}{2} }$

Cross multiply

$23(23)=a*\frac{a}{2}$

$529=\frac{a^2}{2}$

Multiply both sides by 2

$1058=a^2$

Square root both sides

$32.5=a$

I hope this helps and is correct please let me know if it is right and if you have any further questions