Question

please answer me with solution please​

Answer 1

Step-by-step explanation:

AB=AC

AB+BC+AC=259

13x+11x+13x=259

37x=259

x=7

AB=91cm,BC=77cm,AC=91 cm

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Answer 2

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Concept}}}$

Here the concept of Perimeter of the triangle has been used. We see that we are given a isosceles triangle whose sides AB and AC are equal. Even we are given the ratio of two sides. Now using that ratio we can take a constant variable which can be multiplied to the value of ratio so that we can get the values of sides.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{\pink{Sum\;of\;all\;sides\;=\;\bf{Perimeter\;of\;\Delta}}}}$

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★ Solution :-

Given,

» ∆ABC is an isoceles triangle.

» Perimeter of Triangle ABC = 259 cm

» AB = AC

» AB : BC :: 13 : 11

This sign (::) shows proportionality between the sides. This will give us,

✒ AB : BC = 13 : 11

• Let the constant be x with which the numerator and denominator of this ratio should be multiplied to get the answer.

Then using this, we get

→ AB = 13 x

→ BC = 11 x

→ AC = AB = 13

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~ For the value of x ::

We know that,

$\\\;\sf{\rightarrow\;\;Sum\;of\;all\;sides\;=\;\bf{Perimeter\;of\;\Delta}}$

By applying values, we get

$\\\;\sf{\Longrightarrow\;\;AB\;+\;BC\;+\;AC\;=\;\bf{Perimeter\;of\;\Delta\:ABC}}$

$\\\;\sf{\Longrightarrow\;\;13x\;+\;11x\;+\;13x\;=\;\bf{259}}$

$\\\;\sf{\Longrightarrow\;\;26x\;+\;11x\;=\;\bf{259}}$

$\\\;\sf{\Longrightarrow\;\;37x\;=\;\bf{259}}$

$\\\;\sf{\Longrightarrow\;\;x\;=\;\bf{\dfrac{259}{37}}}$

$\\\;\bf{\Longrightarrow\;\;x\;=\;\bf{\red{7}}}$

Hence, we got the value of x = 7

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~ For length of all sides of triangle ABC ::

For finding length, we simply need to apply the value of x we got into the sides.

Then,

$\\\;\bf{\mapsto\;\;AB\;=\;13x\;=\;13(7)\;=\;\green{91\;\:cm}}$

$\\\;\bf{\mapsto\;\;BC\;=\;11x\;=\;11(7)\;=\;\orange{77\;\:cm}}$

$\\\;\bf{\mapsto\;\;AB\;=\;13x\;=\;13(7)\;=\;\blue{91\;\:cm}}$

$\\\;\underline{\boxed{\tt{Hence,\;\:length\;\:of\;\:all\;\:sides\;=\;\bf{\purple{91\;cm,\;77\;cm}\;\tt{and}\;\bf{\purple{91\;cm}}}}}}$

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★ Verification ::

In order to verify our answer, we need to simply apply the value we got, into the equation we formed. Then,

$\\\;\tt{\gray{\leadsto\;\;13x\;+\;11x\;+\;13x\;=\;259}}$

$\\\;\tt{\gray{\leadsto\;\;13(7)\;+\;11(7)\;+\;13(7)\;=\;259}}$

$\\\;\tt{\gray{\leadsto\;\;91\;+\;77\;+\;91\;=\;259}}$

$\\\;\bf{\gray{\leadsto\;\;259\;=\;259}}$

Clearly, LHS = RHS. Here the condition satisfies, so our answer is correct.

Hence, verified.

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★ More to know :-

$\\\;\sf{\leadsto\;\;Area\;of\;Triangle\;=\;\dfrac{1}{2}\:\times\:Base\:\times\:Height}$

$\\\;\sf{\leadsto\;\;Semi\:-\:Perimeter\;of\;\Delta\;=\;\dfrac{Perimeter}{2}}$

$\\\;\sf{\leadsto\;\;Area\;of\;Triangle\;=\;\sqrt{s(s\:-\:a)(s\:-\:b)(s\:-\:c)}}$