Question

the sum of the sides of a right angled triangle containing right angled is 17cm . if its area is 30 sq cm . find the length of the hypotenuese of the triangle​

Answer 1

Answer:

• Two sides of the triangle are 8cm and 15cm.

Given:

• Right angled is 17cm.
• Area of right angled is 30 sq. cm.

To Find:

• Length of the hypotenuse of the triangle = ?

Solution:

Let's assume:

• Let the one side be xcm
• The other side be x+7 cm

As a given triangle is right angled triangle with hypotenuse = 17cm.

By using pythagorus theorem,we get:

$\: \: \sf \: {p}^{2} + {b}^{2} = {h}^{2} \\ \\ \: \: \sf \: {x}^{2} + {(x + 7)}^{2} = {17}^{2} \\ \\ \: \: \sf \: {x}^{2} + {x}^{2} + 14x + 49 - 289 = 0 \\ \\ \: \: \sf \: 2 {x}^{2} + 14x - 240 = 0 \\ \\ \: \: \sf \: {x}^{2} + 7x - 120 = 0 \\ \\ \: \: \sf \: {x}^{2} + 15x - 8x - 120 = 0 \\ \\ \: \: \sf \: x(x + 15) - 8(x + 15) = 0 \\ \\ \: \: \sf \: (x + 15)(x - 8) = 0$

x = -15 or x = 8

x = -15 cannot be negative

x = 8

Hence, the two sides of the triangles are 15cm and 8cm.

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