Question

The perimeter of a right angled triangle is 5 times the length of its shortest side. The numerical value of the area of triangle is 15 times the numerical value of the length of the shortest side. Find the length of the three sides of the triangle

Answer 1

let BC be the shortest side with side x
perimeter = AB + BC + AC
5x = AB + x + AC

area= 1/2(AB)(x)
15x=1/2(AB) (x)
AB=30

rest is given in the photo
therefore AB=30
BC=16
AC=34

Answer 2

Answer:

The length of the three sides of the triangle $AB=30$, $BC=16$ and

$AC=34$.

Step-by-step explanation:

Given:

Perimeter of a right-angled triangle $= 5$ times.

Area of triangle$= 15$ times

To find:

the length of the three sides of the triangle.

Step 1

Let the shortest side $=x$

Area of triangle $=15(x)$

$1 / 2 x y=15 x$

or $y=30$ units

Step 2

The perimeter of a right triangle

$x+y+A C=5 x$

[Given]

$y+A C=4 x$

$\mathrm{AC}=4 \mathrm{x}-30$

Step 3

In $\triangle \mathrm{ABC}$

$A C^{2}=A B^{2}+B C^{2}$

[From $(i)$ and $(ii)$]

$16 x^{2}+900-240 x=900+x^{2}$

$15 x^{2}-240 x=0$

$15 x(x-16)=0$

or $x=16$ units

$A C=4 \times 16-30=34$ units

Therefore, length of the three sides of the triangle

$AB=30$, $BC=16$ and

$AC=34$.

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