Question

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 40cm. Find the length of the hypotenuse

Answer 1

Answer:

17 cm

Step-by-step explanation:

Perimeter = sum of all sides

=> 40 = (8x - 1) + (3x + 2) + (4x + 9)

=> 40 = 8x - 1 + 3x + 2 + 4x + 9

=> 40 = 15x + 10

=> 40 - 10 = 15x

=> 30 = 15x

=> 30/15 = x

=> 2 = x

Sides of the triangle are:

(8x - 1) = 8(2) - 1 = 15

(3x + 2) = 3(2) + 2 = 8

(4x + 9) = 4(2) + 9 = 17

As hypotenuse is the longest side of any triangle, hypotenuse is 17 cm.

Answer 2

Answer:

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,

$\mapsto \rm{\bold{First\: side\: =\: (8x - 1)\: cm}}$

$\mapsto \rm{\bold{Second\: side =\: (3x + 2)\: cm}}$

$\mapsto \rm{\bold{Third\: side =\: (4x + 9)\: cm}}$

As we know that :

$\bigstar\: \: \sf\boxed{\bold{\pink{Perimeter\: of\: triangle =\: Sum\: of\: all\: sides}}}$

Given :

• Perimeter = 40 cm

According to the question by using the formula we get,

$\implies \sf (8x - 1) + (3x + 2) + (4x + 9) =\: 40$

$\implies \sf 8x - 1 + 3x + 2 + 4x + 9 =\: 40$

$\implies \sf 8x + 3x + 4x - 1 + 2 + 9 =\: 40$

$\implies \sf 15x + 1 + 9 =\: 40$

$\implies \sf 15x + 10 =\: 40$

$\implies \sf 15x =\: 40 - 10$

$\implies \sf 15x =\: 30$

$\implies \sf x =\: \dfrac{\cancel{30}}{\cancel{15}}$

$\implies \sf \bold{\purple{x =\: 2}}$

Hence, the required sides are :

$\leadsto$ First side :

$\longrightarrow \sf (8x - 1)\: cm$

$\longrightarrow \sf \{8(2) - 1\}\: cm$

$\longrightarrow \sf (16 - 1)\: cm$

$\longrightarrow \sf\bold{\red{15\: cm}}$

$\leadsto$ Second side :

$\longrightarrow \sf (3x + 2)\: cm$

$\longrightarrow \sf \{3(2) + 2\}\: cm$

$\longrightarrow \sf (6 + 2)\: cm$

$\longrightarrow \sf\bold{\red{8\: cm}}$

$\leadsto$ Third side :

$\longrightarrow \sf (4x + 9)\: cm$

$\longrightarrow \sf \{4(2) + 9\}\: cm$

$\longrightarrow \sf (8 + 9)\: cm$

$\longrightarrow \sf\bold{\red{17\: cm}}$

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 .

VERIFICATION :-

$\implies \tt{(8x - 1) + (3x + 2) + (4x + 9) =\: 40}$

By putting x = 2 we get,

$\implies \tt{\{8(2) - 1\} + \{3(2) + 2\} + \{4(2) + 9\} =\: 40}$

$\implies \tt{ (16 - 1) + (6 + 2) + (8 + 9) =\: 40}$

$\implies \tt{15 + 8 + 17 =\: 40}$

$\implies \tt{\bold{\pink{40 =\: 40}}}$

Hence, Verified.