Question

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11. The lengths of two sides of a right triangle containing the right angle differ by 2 cm. If the
area of the triangle is 24 cm", find the perimeter of the triangle.​

Answer 1

Given :-

★ The lengths of two sides of a right triangle containing the right angle differ by 2 cm.

★ Area of triangle is = 24 cm²

To Find :-

★ Perimeter of the given triangle

Solution :-

Let the triangle be ABC right ( angled at B)

Then,

the length of one side is = x cm =AB

the length of other side is = (x-2) cm =BC

We know,

Area of triangle = ½ × Base ×Height

Substituting the values, we get

24 = ½ × x × (x-2)

⟹ x² -2x -48 =0

⟹ x² - 8x + 6x - 48 =0

⟹ (x -8) (x+6) =0

⟹ x = 8 or -6

Here, length of AB or BC can't be negative.

Therefore,

AB =8 cm

BC = 6 cm

Applying Pythagora's theorem, we have to find AC.

Hence,

AC =√ (AB)² + (BC)²

= √ ( 64 +36)

= 10 cm

Now, perimeter of the given triangle

= 8 + 6 +10

=24 cm

Hence,

perimeter of the triangle is = 24 cm

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