SOLUTION: I need help with the following word problem.... One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the

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Question 49303This question is from textbook
: I need help with the following word problem....
One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?
Thank you! This question is from textbook

Found 2 solutions by Nate, Osran_Shri:
Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!
width(leg) = w
length(leg) = w + 2
diagonal length(hypotenuse) = 10

width = 6 because the width can not be negative
length = 6 + 2 = 8

Answer by Osran_Shri(18) (Show Source):
You can put this solution on YOUR website!
Let one side of a rectangular Stage = A meter
Other side of Rectangula stage = B meter
let us say, A is 2 meter longer than B which means :
A = B + 2 meter
Diagonal D = 10 meters
Apply Pythagoras Theorem : which says : square of A + Square of B = Square of D
in a Rectangle.
Substitute A = B+2 in above equation and rewrite as below:
square of D = square of ( B+2) + square of B
First let us solve : square of ( B + 2)=Sq(B)+Sq(2)+2*B*2=Sq(B)+4+4B
Now : 100 = Sq(B)+4+4B+Sq(B) = 2*Sq(B)+4B+4 let us rewrite as :
100 = 2B^2+4B+4
Now Multiply on eitherside by 2 to give results as below :
200 = 4B^2+8B+8
Now add and subtract 4 on right hand side of the equation to get :
200 = 4B^2 + 8B + 8 + 4 - 4
200 = 4B^2 + 8B + 4 + 4
200 - 4 = 4B^2 + 8B + 4
196 = (2B + 2 )^2
sqrt(196) = 2B + 2
14 = 2B + 2
12 = 2B
B = 6
Therefore answers are : A = B + 2 = 6 + 2 = 8 meter and B= 6 Meter
A = 8 meter / B = 6 meter
How to verify : D^2 = A^2 + B^2
100 = 64 + 36
Thats all.....
By b.Shridhar