Question

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.​

Answer 1

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Let us say, the base of the right triangle be x cm.

Given, the altitude of right triangle = (x – 7) cm

From Pythagoras theorem, we know,

Base^2 + Altitude^2 = Hypotenuse^2

∴ x^2 + (x – 7)^2 = 132

⇒ x^2 + x^2 + 49 – 14x = 169

⇒ 2x^2 – 14x – 120 = 0

⇒ x^2 – 7x – 60 = 0

⇒ x^2 – 12x + 5x – 60 = 0

⇒ x(x – 12) + 5(x – 12) = 0

⇒ (x – 12)(x + 5) = 0

Thus, either x – 12 = 0 or x + 5 = 0,

⇒ x = 12 or x = – 5

Since sides cannot be negative, x can only be 12.

Therefore, the base of the given triangle is 12 cm

and

the altitude of this triangle will be (12 – 7) cm = 5 cm.

Answer 2

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↓↓YOUR ANSWER↓↓

Given, hypotenuse = 13 cm

Let the base be x cm.

Then altitude = (x - 7) cm

Using Pythagoras theorem

♦ (Hypotenuse)² = (Base)² + (Altitude)²

So,

♦ (13)² = ( x )² + ( x - 7 )²

♦ 169 = x² + x² + 49 - 14x

♦ 169 - 49 = 2x² - 14x

♦ 120 = 2 ( x² - 7x )

♦ 120/2 = x² - 7x

♦ 60 = x² - 7x ......(1)

From eq (1)

♦ x² - 7x = 60

♦ x² - 7x - 60 = 0

♦ x² - (12 - 5)x - 60 = 0

♦ x² - 12x + 5x - 60 = 0

♦ x(x - 12) + 5(x - 12) = 0

♦ (x + 5) ( x - 12) = 0

Hence,Value of x

1) x + 5 = 0

x = -5

which is not possible because x is length.

2) x - 12 = 0

x = 12

So,the value of x is 12 cm.

Hence, Altitude = 12 - 7 = 5 cm

And x is base itself = 12 cm

❤!!HOPE IT HELPS YOU!!❤