Question

d. The perimeter of a right angled triangle is 24 and its area is 24. find the sided of the triangle​

Answer 1

Step-by-step explanation:

Let ABC is a right angled triangle.

i) Perimeter of ∆ABC = 24

=> x+y+10=24

=> x+y = 24-10

=> x+y = 14 ---(1)

ii)By Phythagorean theorem:

AC²= AB²+BC²

=> 10²= x² + y²

=> x²+y² = 100 ---(2)

iii) On Squaring equation (1), we get

=> (x+y)² = 14²

=> x²+y²+2xy = 196

=> 100+2xy = 196

/* From (2) */

=> 2xy = 196-100

=> 2xy = 96

/* Divide both sides by 2 , we get

=> xy = 48 ---(3)

Now ,

\begin{gathered}Area \: of \: \triangle ABC = \frac{1}{2} \times AB \times BC\\=\frac{1}{2}\times xy\\=\frac{1}{2}\times 48\end{gathered}

Areaof△ABC=

2

1

×AB×BC

=

2

1

×xy

=

2

1

×48

/* From (3) \

= 24\: cm^{2}=24cm

2

Therefore,

Area \: of \: the\:triangle =24\: cm^{2}Areaofthetriangle=24cm

2

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