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

The area of the right triangle is
`43.88\ cm^(2)`

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)`