Question

The hypotenuse of a right angled triangle is 15 cm. Taking the perpendicular sides as x, y write the
relation connecting the sides ?
If the area is 30cm2
find the length of its perpendicular sides ?

Answer 1

Answer:

your answer is 45=36. subwoofer area side

Answer 2

Given,

Hypotenuse of right angles triangle $\[ = 15cm\]$

Other sides are x and y.

Area of triangle $\[ = 30c{m^2}\]$

Solution,

Relation connecting the sides ?

$\[\begin{array}{l}{x^2} + {y^2} = {15^2}\\ \Rightarrow {x^2} + {y^2} = 225\end{array}\]$--------(1)

If the area is $\[30c{m^2}\]$  find the length of its perpendicular sides ?

$\[\begin{array}{l}\frac{1}{2}xy = 30\\ \Rightarrow xy = 60\end{array}\]$----------(2)

Apply equation 1 and 2,

$\[\begin{array}{l}{\left( {x + y} \right)^2} = {x^2} + {y^2} + 2xy\\ \Rightarrow {\left( {x + y} \right)^2} = 225 + 2 \times 60\\ \Rightarrow {\left( {x + y} \right)^2} = 345\\ \Rightarrow x + y = 18.57\end{array}\]$-----------(3)

$\[\begin{array}{l}{\left( {x - y} \right)^2} = {x^2} + {y^2} - 2xy\\ \Rightarrow {\left( {x - y} \right)^2} = 225 - 2 \times 60\\ \Rightarrow {\left( {x - y} \right)^2} = 105\\ \Rightarrow x - y = 10.24\end{array}\]$------------(4)

Solve equation 3 and 4,

$\[\begin{array}{l}x = 14.41cm\\y = 4.163cm\end{array}\]$

Hence the length of perpendicular side is $\[14.41cm\]$.