Question

sides of a right angle triangle are '5x'm (3x-1)m if the area is 60m^²
find the hypotnues.. ​

Answer 1

Given :-

• Sides of a right trianlge = 5xm and (3x- 1)m

• Area of right angled trianlge = 60m²

To find :-

• Hypotenuse of right angled trianlge

Solution :-

• As we know that

→ Area of trianlge = ½ × base × height

• Base = 5xm
• Height = (3x - 1)m

→ 60 = ½ × 5x × (3x - 1)

→ 60 × 2 = 5x(3x - 1)

→ 120 = 15x² - 5x

→ 15x² - 5x - 120 = 0

• Take 5 as a common

→ 5(3x² - x - 24) = 0

→ 3x² - x - 24 = 0

→ 3x² - 9x + 8x - 24 = 0

→ 3x(x - 3) + 8(x - 3) = 0

→ (x - 3)(3x + 8) = 0

• Either

→ x - 3 = 0

→ x = 3

• Or

→ 3x + 8 = 0

→ x = - 8/3

Note :

• Length never in negative

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•°• Base = 5x = 15m

•°• Height = 3x - 1 = 3 × 3 - 1 = 8m

• According to Pythagoras theorem

(hypotenuse)² = (base)² + (perpendicular)²

→ (h)² = (b)² + (p)²

→ h² = (15)² + (8)²

→ h² = 225 + 64

→ h² = 289

→ h = √289

→ h = 17m

•°• Hypotenuse of right angled trianlge = 17m

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Answer 2

$\huge{ \boxed{ \sf{ \purple{Question?}}}}$

Sides of a right angle triangle are '5x'm (3x-1)m if the area is 60m² find the hypotenues.

$\huge{ \boxed{ \sf{ \orange{Answer:- }}}}$

Hypotenues of triangle is 17m.

$\huge{ \boxed{ \sf{ {Explanation:- }}}}$

Given:-

• Sides of a right angle triangle are '5x'm (3x-1)m.
• Area is 60m²

To Find:-

• Find the hypotenues

Finding it:-

• Formula used:-

${ \bigstar{\sf{ Area \: of \: triangle = \frac{1}{2} \times base \times height}}}$

• Base- 5x m
• Height- 3x-1 m
• Area- 60m²

• So now let's solve it..!

${ \implies{\sf{ 60= \frac{1}{2} \times 5x \times 3x - 1}}}$

${ \implies{\sf{ 60 \times 2= 5x \times 3x - 1}}}$

${ \implies{\sf{ 120= {15x}^{2} - 5x}}}$

${ \implies{\sf{ {15x}^{2} - 5x - 120 = 0}}}$

${ \implies{\sf{5 ({3x}^{2} - x - 24)= 0}}}$

${ \implies{\sf{ ({3x}^{2} - x - 24)= 0}}}$

${ \implies{\sf{ x - 3 \times 3x + 8 = 0}}}$

• Here, there will be 2 answers-

${ \implies{\sf{ x - 3 = 0}}}$

${ \implies{\sf{ x = 3}}}$

• Second answers-

${ \implies{\sf{ 3x + 8 = 0}}}$

${ \implies{\sf{ 3x = - 8}}}$

${ \implies{\sf{ x = - \frac{ 8}{3} }}}$

• Here always remember that lenght can never be a negative value. So the second answer will not be applicable.

$\implies \sf{base = 5x = 15m}$

$\implies \sf{height = 3x - 1=3 \times 3 - 1 = 8m}$

Now by using the Pythagoras theorem:-

$\implies \sf Hypotenues² = Perpendicular² + Base² </u></p><p><u>[tex] \implies \sf Hypotenues² = Perpendicular² + Base²$

$\implies \sf {h}^{2} = {p}^{2} + {b}^{2}$

$\implies \sf {h}^{2} = {15}^{2} + {8}^{2}$

$\implies \sf {h}^{2} = {225}+ {64}$

$\implies \sf {h}^{2} = 289$

$\implies \sf {h} = \sqrt{289}$

$\implies \sf {h} = 17m$

So, the hypotenues of triangle is 17m.

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