Hello from MrBillDoesMath!
Answer:
b = 25
h = 7
Discussion:
Given: A = bh = 175
From the diagram: b = 4x+1 and h = x + 1. Substituting these in the formula for Area gives
(4x +1) (x+1 ) = 175 =>
(4x + 1 )* x + (4x + 1)*1 = 175 =>
(4x^2 + x) +(4x + 1) = 175 =>
4x^2 + 5x + 1 - 175 = 0 =>
4x^2 + 5x - 174 = 0
Via the rational root theorem ( roots are of form p/q where p is a factor of 174 ( +\-2, +\-3, +\-29 and q is a factor of 4 (+\-2) ) we find that x = 6.
Hence b = 4x + 1 = 4(6) + 1 = 25 and h = x+1 = 6+1 = 7
Regards,
MrB
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