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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