Question

The sides of a right-angled triangle containing the right angle at 5x cm and (3x-1) cm. Calculate the length of the hypotenuse of th triangle of its area is 60cm^2

Answer 1

x=3,hyp=√289=17.......

Answer 2

Consider ABC as a right angled triangle

AB = 5x cm and BC = (3x – 1) cm

We know that

Area of △ABC = ½ × AB × BC

Substituting the values

60 = ½ × 5x (3x – 1)

By further calculation

120 = 5x (3x – 1)

120 = 15x2 – 5x

It can be written as

15x2 – 5x – 120 = 0

Taking out the common terms

5 (3x2 – x – 24) = 0

3x2 – x – 24 = 0

3x2 – 9x + 8x – 24 = 0

Taking out the common terms

3x (x – 3) + 8 (x – 3) = 0

(3x + 8) (x – 3) = 0

Here

3x + 8 = 0 or x – 3 = 0

We can write it as

3x = -8 or x = 3

x = -8/3 or x = 3

x = -8/3 is not possible

So x = 3

AB = 5 × 3 = 15 cm

BC = (3 × 3 – 1) = 9 – 1 = 8 cm

In right angled △ABC

Using Pythagoras theorem

AC2 = AB2 + BC2

Substituting the values

AC2 = 152 + 82

By further calculation

AC2 = 152 + 82

By further calculation

AC2 = 225 + 64 = 289

AC2 = 172

So AC = 17 cm

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