Question

De un triángulo rectángulo se conoce que su hipotenusa mide 20 cm y la suma de los catetos miden 24 cm ¿Cuánto mide su área?

Answer 1

Answer:

The area of the right triangle is $43.88\ cm^{2}$

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

$20^{2}=x^{2}+y^{2}$ -----> equation A

$x+y=24$

$y=24-x$ -----> equation B

Substitute equation B in equation A and solve for x

$20^{2}=x^{2}+(24-x)^{2}\\ \\400=x^{2} + 576-48x+x^{2}\\ \\ 2x^{2} -48x+576-400=0\\ \\2x^{2} -48x+176=0$

Solve the quadratic equation by graphing

The solution is  $x=4.5\ cm$  

see the attached figure

$x=4.5\ cm$

$y=24-4.5=19.5\ cm$

The area is equal to

$A=xy/2=(4.5)(19.5)/2=43.88\ cm^{2}$