Answer:
The area of the right triangle is [tex]43.88\ cm^{2}[/tex]
Step-by-step explanation:
The question in English is
From a right triangle it is known that its hypotenuse measures 20 cm and the sum of the legs measures 24 cm. How much does its area measure?
Let
x-----> the measure of one leg
y----> the measure of the other leg
Assume x is less than y
we know that
Applying Pythagoras Theorem
[tex]20^{2}=x^{2}+y^{2}[/tex] -----> equation A
[tex]x+y=24[/tex]
[tex]y=24-x[/tex] -----> equation B
Substitute equation B in equation A and solve for x
[tex]20^{2}=x^{2}+(24-x)^{2}\\ \\400=x^{2} + 576-48x+x^{2}\\ \\ 2x^{2} -48x+576-400=0\\ \\2x^{2} -48x+176=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]x=4.5\ cm[/tex]
see the attached figure
[tex]x=4.5\ cm[/tex]
[tex]y=24-4.5=19.5\ cm[/tex]
The area is equal to
[tex]A=xy/2=(4.5)(19.5)/2=43.88\ cm^{2}[/tex]
