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Answers
Explanation:
Given :-
The sides of a right angled triangle are (8x - 1) cm (3x + 2) cm and (4x + 9) cm if the perimeter of the triangle is 40 cm.
To Find :-
What is the length of the hypotenuse.
Solution :-
Let,
\mapsto \rm{\bold{First\: side\: =\: (8x - 1)\: cm}}↦Firstside=(8x−1)cm
\mapsto \rm{\bold{Second\: side =\: (3x + 2)\: cm}}↦Secondside=(3x+2)cm
\mapsto \rm{\bold{Third\: side =\: (4x + 9)\: cm}}↦Thirdside=(4x+9)cm
As we know that :
\begin{gathered}\bigstar\: \: \sf\boxed{\bold{\pink{Perimeter\: of\: triangle =\: Sum\: of\: all\: sides}}}\\\end{gathered}
★
Perimeteroftriangle=Sumofallsides
Given :
Perimeter = 40 cm
According to the question by using the formula we get,
\implies \sf (8x - 1) + (3x + 2) + (4x + 9) =\: 40⟹(8x−1)+(3x+2)+(4x+9)=40
\implies \sf 8x - 1 + 3x + 2 + 4x + 9 =\: 40⟹8x−1+3x+2+4x+9=40
\implies \sf 8x + 3x + 4x - 1 + 2 + 9 =\: 40⟹8x+3x+4x−1+2+9=40
\implies \sf 15x + 1 + 9 =\: 40⟹15x+1+9=40
\implies \sf 15x + 10 =\: 40⟹15x+10=40
\implies \sf 15x =\: 40 - 10⟹15x=40−10
\implies \sf 15x =\: 30⟹15x=30
\implies \sf x =\: \dfrac{\cancel{30}}{\cancel{15}}⟹x=
15
30
\implies \sf \bold{\purple{x =\: 2}}⟹x=2
Hence, the required sides are :
\leadsto⇝ First side :
\longrightarrow \sf (8x - 1)\: cm⟶(8x−1)cm
\longrightarrow \sf \{8(2) - 1\}\: cm⟶{8(2)−1}cm
\longrightarrow \sf (16 - 1)\: cm⟶(16−1)cm
\longrightarrow \sf\bold{\red{15\: cm}}⟶15cm
\leadsto⇝ Second side :
\longrightarrow \sf (3x + 2)\: cm⟶(3x+2)cm
\longrightarrow \sf \{3(2) + 2\}\: cm⟶{3(2)+2}cm
\longrightarrow \sf (6 + 2)\: cm⟶(6+2)cm
\longrightarrow \sf\bold{\red{8\: cm}}⟶8cm
\leadsto⇝ Third side :
\longrightarrow \sf (4x + 9)\: cm⟶(4x+9)cm
\longrightarrow \sf \{4(2) + 9\}\: cm⟶{4(2)+9}cm
\longrightarrow \sf (8 + 9)\: cm ⟶(8+9)cm
\longrightarrow \sf\bold{\red{17\: cm}}⟶17cm
As we know that :
\leadsto⇝ Length of Hypotenuse :
Hypotenuse is the longest side of a right-angled triangle.
\therefore∴ The length of hypotenuse of a right-angled triangle is 17 cm .