Question

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Answer 1

Answer:

Hypotenuse = 17 cm

Base = 15 cm

Perpendicular = 8 cm

Step-by-step explanation:

Let the base, altitude and hypotenuse of a right angled triangle be b, p and h respectively.

A.T.Q.

Hypotenuse = Base + 2

Equation formed : h = b + 2

→ b = h - 2

....(1)

Also,

Hypotenuse = 2(Perpendicular) + 1

Equation formed : h = 2p + 1

→ 2p = h - 1

→ $\sf{p = {\dfrac{h - 1}{2}}}$

....(2)

We know that,

(Hypotenuse)² = (Base)² + (Perpendicular)²

→ (h)² = (b)² + (p)²

→ h² = (h - 2)² + ($\sf{{\dfrac{h - 1}{2}}}$)²

Identity : (a - b)² = a² - 2ab + b²

→ h² = [(h)² - 2(h)(2) + (2)²] + [ $\sf{{\dfrac{(h)^2 - 2(h)(1) + (1)^2}{(2)^2}}}$ ]

→ h² = h² - 4h + 4 + $\sf{{\dfrac{h^2 - 2h + 1}{4}}}$

→ h² = $\sf{{\dfrac{4h^2 - 16h + 16 + h^2 - 2h + 1}{4}}}$

→ 4h² = 4h² - 16h + 16 + h² - 2h + 1

→ 4h² - 4h² = h² - 16h - 2h + 16 + 1

→ 0 = h² - 18h + 17

Using Middle Term Factorisation

→ 0 = h² - 17h - h + 17

→ 0 = h(h - 17) - 1(h - 17)

→ 0 = (h - 1)(h - 17)

Using Zero Product Rule

→ (h - 1) = 0 and (h - 17) = 0

→ h = 1 and h = 17

• If h = 1, then

b = h - 2

= 1 - 2

= - 1

Base can't be in negative value. Hence, h = 17.

When h = 17, then

b = h - 2

= 17 - 2

= 15

p = $\sf{{\dfrac{h - 1}{2}}}$

= $\sf{{\dfrac{17 - 1}{2}}}$

= $\sf{{\dfrac{16}{2}}}$

= 8

Therefore,

Hypotenuse = 17 cm

Base = 15 cm

Perpendicular = 8 cm

Verification :

As we know that,

(Base)² + (Perpendicular)² = {Hypotenuse)

L.H.S. = (Base)² + (Perpendicular)²

= (15)² + (8)²

= 225 + 64

= 289

R.H.S. = (Hypotenuse)²

= (17)²

= 289

L.H.S. = R.H.S.

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