MartinTao wrote:
The hypotenuse of a right triangle is 16 ft longer than the length of the shorter leg. If the area of this triangle is exactly 120 ft², what is the length of the hypotenuse in feet?
A. 26
B. 32
C. 40
D. 64
E. 80
Another way is working with triangle properties.
We know that the
sum of two sides must be greater than the third side. Let's work with this:
short leg: a
long leg: b
hypotenuse: c=a+16
This means, the long leg has to be longer than 16 ft.
Now, we factorize 240 (which is a*b).
\(240=2^4*3*5\)
\(2^4\) is \(16\), but we need greater than \(16\), so lets try \(2^3*3=24=b\).
In this case \(a=10, b=24, c=26\).
\(a+b>c...10+24=34>26\)
\(a+c>b...10+26=36>24\)
\(b+c>a...24+26=50>10\)
Answer (A)