The hypotenuse of a right-angled triangle measures 65 cm and its base is 60 cm.

Question:

The hypotenuse of a right-angled triangle measures 65 cm and its base is 60 cm. Find the length of perpendicular and the area of the triangle.

 

Solution:

Hypotenuse = 65 cm
​Base = 60 cm
In a right-angled triangle,

$(\text { Hypotenuse })^{2}=(\text { B ase })^{2}+(\text { P erpendicular })^{2}$

$\Rightarrow(65)^{2}=(60)^{2}+(\text { perpendicular })^{2}$

$\Rightarrow(65)^{2}-(60)^{2}=(\text { perpendicular })^{2}$

$\Rightarrow(\text { perpendicular })^{2}=(65-60)(65+60)$

$\Rightarrow(\text { perpendicular })^{2}=5 \times 125$

$\Rightarrow(\text { perpendicular })^{2}=625$

$\Rightarrow$ perpendicular $=25 \mathrm{~cm}$

Area of triangle $=\frac{1}{2} \times$ base $\times$ perpendicular

$=\frac{1}{2} \times 60 \times 25$

$=750 \mathrm{~cm}^{2}$

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