SOLUTION: i badly needed your precious help, please i think i'm going to die. my problem is the school stage is rectangular in shape. its diagonal is 13 m. the length is 7m longer than its

Question 556184: i badly needed your precious help, please i think i'm going to die. my problem is the school stage is rectangular in shape. its diagonal is 13 m. the length is 7m longer than its width. find the length and width of the stage.. please i really need your answer
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
diagonal is 13 meters.
length is 7 meters longer than than the width.
let x = width.
this makes the length x + 7
diagonal and the length of the stage and the width of the stage form a right triangle whose hypotenuse is 13 meters in length.
using formula by pythagorus, we get:
hypotenuse squared = length squared plus width squared.
this becomes:
13^2 = (x+7)^2 + x^2 which becomes:
169 = x^2 + 14x + 49 + x^2 which becomes:
169 = 2x^2 + 14x + 49
subtract 169 from both sides of this equation to get:
2x^2 + 14x + 49 - 169 = 0
combine like terms to get:
2x^2 + 14x - 120 = 0
divide both sides of this equation by 2 to get:
x^2 + 7x - 60 = 0
factor this quadratic equation to get:
(x-5) * (x+12) = 0
solve for x to get:
x = -12 or x = 5
x can't be negative so your answer has to be:
x = 5
that means the width of the stage is 5 meters.
it also means that the length of the stage is 12 meters.
using pythagorus relationship, we get:
13^2 = 5^2 + 12^2 = 25 + 144 = 169
this confirms the values for the length and width of the stage are good.
the following diagram shows you what i mean:
$$$$

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