Question

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

Answer 1

$\huge\underline\mathbb{SOLUTION:-}$

$\mathsf {Let,\:base\:of\:triangle\:be\:x}$

$\mathsf {And, \:Let\:altitude\:of\:triangle\:be\:(x - 7)\:Cm}$

$\mathsf {It\:is\:given\:that\:hypotenuse\:of\:triangle\:is\:13\:Cm}$

$\underline \texttt {According\:to\:Pythagoras\:Theorem,}$

$\mathsf {13^2 = x^2 + (x - 7)^2 \: \:(a + b)^2 = a^2 + b^2 + 2ab}$

$\implies \mathsf {169 = x^2 + x^2 + 49 - 14x}$

$\implies \mathsf {169 = 2x^2 - 14x + 49}$

$\implies \mathsf {2x^2 - 14x - 120 = 0}$

$\underline \texttt {Dividing\:equation\:by\:2}$

$\implies \mathsf {x^2 - 7x - 60 = 0}$

$\implies \mathsf {x^2 - 12x + 5x - 60 = 0}$

$\implies \mathsf {X(x - 12) + 5(x -12) = 0}$

$\implies \mathsf {(x - 12) (x + 5}$

$\implies \mathsf {x = -5,\:12}$

$\mathsf {We\:discard\:x = -5\:because\:length\:of\:side\:of}$

$\mathsf {triangle\:cannot\:be\:negative.}$

$\therefore \mathsf \blue {Base\:of\:triangle = 12\:Cm}$

$\mathsf \blue {Altitude\:of\:triangle = (x - 7) = 12 - 7 = 5\:Cm}$

Answer 2

Answer:

Let,baseoftrianglebex

\mathsf {And, \:Let\:altitude\:of\:triangle\:be\:(x - 7)\:Cm}And,Letaltitudeoftrianglebe(x−7)Cm

\mathsf {It\:is\:given\:that\:hypotenuse\:of\:triangle\:is\:13\:Cm}Itisgiventhathypotenuseoftriangleis13Cm

\underline \texttt {According\:to\:Pythagoras\:Theorem,}

AccordingtoPythagorasTheorem,

\mathsf {13^2 = x^2 + (x - 7)^2 \: \:(a + b)^2 = a^2 + b^2 + 2ab}13

2

=x

2

+(x−7)

2

(a+b)

2

=a

2

+b

2

+2ab

\implies \mathsf {169 = x^2 + x^2 + 49 - 14x}⟹169=x

2

+x

2

+49−14x

\implies \mathsf {169 = 2x^2 - 14x + 49}⟹169=2x

2

−14x+49

\implies \mathsf {2x^2 - 14x - 120 = 0}⟹2x

2

−14x−120=0

\underline \texttt {Dividing\:equation\:by\:2}

Dividingequationby2

\implies \mathsf {x^2 - 7x - 60 = 0}⟹x

2

−7x−60=0

\implies \mathsf {x^2 - 12x + 5x - 60 = 0}⟹x

2

−12x+5x−60=0

\implies \mathsf {X(x - 12) + 5(x -12) = 0}⟹X(x−12)+5(x−12)=0

\implies \mathsf {(x - 12) (x + 5}⟹(x−12)(x+5

\implies \mathsf {x = -5,\:12}⟹x=−5,12

\mathsf {We\:discard\:x = -5\:because\:length\:of\:side\:of}Wediscardx=−5becauselengthofsideof

\mathsf {triangle\:cannot\:be\:negative.}trianglecannotbenegative.

\therefore \mathsf \blue {Base\:of\:triangle = 12\:Cm}∴Baseoftriangle=12Cm

\mathsf \blue {Altitude\:of\:triangle = (x - 7) = 12 - 7 = 5\:Cm}Altitudeoftriangle=(x−7)=12−7=5Cm

Step-by-step explanation:

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