we have the following dimensions:
w=wide
w+70=length
We have a right triangle:
leg₁=w
leg₂=w+70
hypotenuse=130
Pythagoras theorem:
leg₁²+leg₂²=hypotenuse²
Then:
w²+(w+70)²=130²
We have to solve that equation:
w²+(w+70)²=130²
w²+w²+140w+4900=16900
2w²+140w+4900-16900=0
2w²+140w-12000=0
(2w²+140w-12000)/2=0/2
w²+70w-6000=0
w=(-70⁺₋√(4900+24000)) / 2
=(-70⁺₋170) / 2
We have two possible solutions:
Solution 1
w=(-70-170)/2=-120 (this solution is not possible because the result is negative and it have no sense in this problem).
Solution 2
w=(-70+170)/2=50 (this is the right solution)
w=50
w+70=120
ANSWER: the length would be 120 u (u=units of length ) and the wide would be 50 u.
