Answer the 15th question. { NO LINKS }.{ NO ANSWERS FROM GOOGLE }.
Q.15. If the perimeter of a right angled triangle is 60 cm and its hypotenuse is 25 cm, find its area.

Dear Student,

The given right angled triangle is as under:



where the base is $x$ and the perpendicular is $y$

Since, hypotenuse is 25, thus using Pythagoras theorem, 

$$\begin{gathered} x^2+y^2={25}^2 \\ {x}^2+y^2=625.....\left(i\right) \end{gathered}$$

As, perimeter is 60, given in the question, therefore,

$$\begin{gathered} x+y+25=60 \\ x+y=35.....\left(ii\right) \end{gathered}$$

squaring both the sides, in equation (ii),

$$\begin{gathered} {\left(x+y\right)}^2={\left(35\right)}^2 \\ {x}^2+y^2+2xy=1225 \end{gathered}$$

Replacing the values of $x^2+y^2$ from equation (i),
$$\begin{gathered} 625+2xy=1225 \\ 2xy=600 \\ xy=300 \end{gathered}$$

Hence, area of the right angled triangle is;

$$\begin{gathered} =\frac{1}{2}xy \\ =\frac{1}{2}\times 300 \\ =150 \end{gathered}$$

Hope this information will clear your doubts about the topic.

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