Question

If the difference between the two sides (other than the longest side) of a right angled triangle is 2 cm and the area of the triangle is 24 sq. cm, then the longest side of the given triangle is​

Answer 1

Answer:

length of hypotenuse(longest side) is $10cm$

Step-by-step explanation:

Let AB $=x$

BC$=y$

hypotenuse AC$=z$

According to question,

$AB-BC=2$

$x-y=2$

$x=2+y$

Area of triangle is given by $=\frac{1}{2} bh$

                                              $24 = \frac{1}{2} xy$

substituting value of x

$48 = (2+y)y$

$48 = 2y + y^{2}$

$y^{2} + 2y -48=0$

$y^{2} + 8y - 6y - 48=0$

$y(y+8)-6(y+8)=0$

$(y+8)(y-6)=0$

∴$y=-8\\y=6$

Side of triangle cannot be negative.

So, $BC=6cm$

$AB=x=y+2$

$AB=8cm$

applying pythagoras theorem to calculate value of hypotenuse,

$x^{2} +y^{2} =z^{2}$

$8^{2} + 6^{2} =z^{2}$

$64+36=z^{2}$

$z=\sqrt{100}$

$z=$±$10$

Hence, length of hypotenuse(longest side) is $10cm$