The perimeter of a right angled
triangle is 40cm. Its hypotenuse
is 17 cm. Find the sides containing
the right angle. Also find the area.
Answers
Answer:
60cm
Step-by-step explanation:
The area is 60 cm^2. Here’s one way of getting the answer:
First we’ll use the information about the perimeter to get side b in terms of side a:
a + b + 17 = 40
a + b = 40 - 17 = 23
b = 23 - a
Next we’ll use the Pythagorean equation for the hypotenuse to get a quadratic equation in a, which we know we’ll be able to then solve to get a and b:
a^2 + (23 - a)^2 = 17^2
a^2 + 529 - 46a + a^2 = 289
2a^2 - 46a - 240 = 0
a^2 - 23a + 120 = 0
We could use the general solution for quadratic equation (you know -b = or - sqrt(b^2–4ac) all divided by 2a), but I see that 15 * 8 = 120 and 15+8 = 23. So,
(a-15)(a-8) =0
a=15 and b = 23 -15 = 8 or a=8 and b = 23–8 = 15. Take your pick. It won’t matter in finding the area.
(Let’s double check our answers first. 8^2 + 15^2 = 64 + 225 = 289 = 17^2 and 8+15+17=40
Incidentally, 8,15,17 is an instance of a Pythagorean triple, since all sides of the triangle are integers (rather than an expression like 5sqrt2.)
Since we’re dealing with a right triangle, the area is ab/2. (Now you see why it doesn’t matter what we pick for a or b since ab = ba.)
area = 8*15/2 = 60
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