Question

The hypotenuse of a right - angled triangle is 17 cm and the different between other two sides is 7 cm. Find the other two unknown sides.​

Answer 1

❍ Let the shorter side be x cm.

━━━━━━━━━━━━━━━━━

☆ Since the difference between the two sides is 7 cm,

∴ longer side = (x + 7) cm.

As the given triangle is right - angled with hypotenuse = 17 cm, by using Pythagoras theorem, we get

➝ x² + (x + 7)² = (17)²

➝ x² + x² + 14x + 49 = 289

➝ 2x² + 14x - 240 = 0

➝ x² + 7x - 120 = 0

➝ x² + 15x - 8x - 120 = 0

➝ x (x + 15) - 8(x + 15) = 0

➝ (x + 15) (x - 8) = 0

➝ x + 15 = 0 or x - 8 = 0

➝ x = -15 or x = 8

But x cannot be negative,

∴ x = 8

⚘ Therefore,

• Hence, the two sides of the triangle are 8 cm and (8 + 7) cm i.e. 15 cm.

━━━━━━━━━━━━━━━━━

Answer 2

Given :

• Hypotenuse, H = 17 cm
• Difference between base and perpendicular = 7 cm

To Find :

• Perpendicular, P = ?
• Base, B = ?

Solution :

Let Base be "x"

As, difference between base and perpendicular = 7 cm.

So, Perpendicular = x + 7 cm

Now, by using Pythagoras Therom :

[H² = B² + P²]

=> (17)² = x² + (x + 7)²

=> 289 = x² + x² + (7)² + 2 × x × 7

=> 289 = 2x² + 49 + 14x

=> 0 = 2x² + 14x - 289 + 49

=> 0 = 2x² + 14x - 240

=> 0 = 2(x² + 7x - 120)

=> x² + 7x - 120 = 0

=> x² + 15x - 8x - 120 = 0

=> x(x + 15) - 8(x + 15) = 0

=> (x - 8) (x + 15) = 0

=> x - 8 = 0 ; x + 15 = 0

=> x = 8 ; x = - 15

As, sides can't be negative.

So, x = - 15 will be rejected.

Hence, x = 8

So,

• Base = 8 cm
• Perpendicular = 8 + 7 = 15 cm