Question

The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides.

Answer 1

Hypotenuse = 26 cm
The sum of other two sides is 34 cm.
So, let the other two sides be x cm and (34 – x) cm.
Using Pythagoras theorem,
${26}^2=x^2+(34–x{)}^2$
$676=x^2+x^2+1156–68x$
$2x^2–68x+480=0$
$x^2–34x+240=0$
$x^2–10x–24x+240=0$
$x(x–10)–24(x–10)=0$
$(x–10)(x–24)=0$
x = 10, 24
When x = 10, (34 – x) = 24
When x = 24, (34 – x) = 10
Thus, the lengths the three sides of the right-angled triangle are 10 cm, 24 cm and 26 cm.