SOLUTION: what rectangle has a perimeter of 30 units and an area of 50 units squared?

Question 254172: what rectangle has a perimeter of 30 units and an area of 50 units squared?
Found 2 solutions by drk, solver91311:
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
Perimeter is 2l + 2w
area is lw
From this ,we have
(i) 2l+2w = 30
(ii) lw = 50
From (i) we get
(ii) l + w = 15
Solve for l to get
(iv) l = 15-w.
Substitute (iv) into (ii) to get
(v) (15-w)(w) = 50
Now,
-w^2 + 15w = 50
and
w^2 - 15w + 50 = 0
(w-10)(w-5) = 0
So, W = 10 or W = 5.
If W = 10, L = 5
If W = 5, L =10
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let represent the width and let represent the length.

The perimeter is:

Which can be solved for :

(verification of that last step is left as an exercise for the student)

The area is the length times the width, so:

Substituting:

Rearrange to standard form:

Just solve the factorable quadratic. The width will be one of the roots and the length will be the other.

John

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