SOLUTION: The diagonal of a rectangle field is y^2+16cm and one side is 8y cm. For what value of y the perimeter of the rectangle will be 62 cm
I. 3cm II.5cm III.7cm
I
II
I AND II
II AN
Algebra.Com
Question 1133678: The diagonal of a rectangle field is y^2+16cm and one side is 8y cm. For what value of y the perimeter of the rectangle will be 62 cm
I. 3cm II.5cm III.7cm
I
II
I AND II
II AND III
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
The diagonal of a rectangle field is cm and one side is cm. For what value of y the perimeter of the rectangle will be cm
To find the width, multiply the length that you have been given by, and subtract the result from the perimeter. You now have the total length for the remaining sides. This number divided by is the width.
diagonal cuts rectangle into two right triangles, so if
, , and we have
if =>=>....one solution to use
if =>....another solution to use
=>=> , .....disregard these solutions
go with:
=>
and
=> disregard negative solution
go with:
=>
and
check the perimeter:
diagonal:
so, your answer is: I.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Solving the problem formally using algebra gets quite messy, as you can see in the solution from the other tutor. And it involves finding the roots of a 4th degree polynomial, which involves some trial and error with synthetic division.
The way the problem is presented, with answer choices, it makes FAR more sense simply to see which answers work. y = 3, 5, and 7 all give right triangles that are Pythagorean triples; but only y = 3 gives a perimeter of 62 for the rectangle.
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