SOLUTION: 1. If the perimeter of a rectangle is 26 meters, and the area is 30 square meters, what is the diagonal? 2. A right triangle has area 30 square meters and perimeter 30 meters

Question 262938: 1. If the perimeter of a rectangle is 26 meters, and the area is 30 square meters,
what is the diagonal?
2. A right triangle has area 30 square meters and perimeter 30 meters. What is
its hypotenuse?
I understand how to do #1 (via quadratic equation), but I don't see how to set-up #2, with the triangle perimeter info. The solution must be under my nose, but I just don't see it (as of yet).
Thank you.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
If the perimeter of a rectangle is 26 meters, and the area is 30 square meters,
what is the diagonal?
2. A right triangle has area 30 square meters and perimeter 30 meters. What is
its hypotenuse?
I understand how to do #1 (via quadratic equation), but I don't see how to set-up #2, with the triangle perimeter info. The solution must be under my nose, but I just don't see it (as of yet).
Thank you.
1. Perimeter of triangle = 2*(l+w)
26= 2*(l+w)
13= l+w
LB =30
Let length be x
Width = 13-x
X*(13-x)= 30
13x-x^2=30
X^2-13x+30=0
X^2-10x-3x+30=0
X(x-10)-3(x-10)=0
(x-10)(x-3) =0
X=3 or 10 The length and breadth can be said to be 10 and 3 meters

2. Area of right triangle =30 square meters

�a + b + h = 30 a and b are the sides and h the hypo
(1 / 2) a b = 30 or a b = 60
a 2 + b 2 = h 2
�Rewrite the equation a + b + h = 60 as follows
a + b = 30 - h
�Square both sides
(a + b)2 = (30 - h)2
�Expand both sides
a2 + b2 + 2 a b = 302 + h2 - 60 h
�Combine the equation a 2 + b 2 = h 2 with the above equation to obtain
2 a b = 302 - 60 h
�a b is known to be equal to 60, hence the above equation becomes
120 = 302 - 60 h
�Solve for h to obtain
h = 13 units
�Substitute h by 13 in the equation a + b + h = 60 to obtain
a + b +13=30 =17
�Since a b = 60, then b = 60 / a which is substituted in the equation a + b = 60 to obtain
a + 60 / a - 17 = 0
�Multiply all terms by a to obtain a quadratic equation of the form
a 2 + 60 - 17 a = 0
�Solve the above equation to obtain two solutions
a^2-17a+60=0
Use the equation a b = 60 to obtain
when a 12 , b = 5 and when a = 5 , b =12
�The two sides of the right triangle and the hypotenuse are, respectively, given by
5 units, 12 units and 13 units.
mananth@hotmail.com

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