Question

Solve- cbb to work it out

Answer 1

Answers:

Hypotenuse of triangle ( a ) = 21.63 mm

Hypotenuse of triangle ( b ) = 150 mm

Hypotenuse of triangle ( c ) = 111.80 mm

Step-by-step explanation :

find the length of hypotenuse in the given 3 triangles, which can be done by using Pythagoras theorem.

`h^2 = b^2 + p^2`

And we have to convert the answer to the units indicated in red i.e, in mm.

Since 1cm = 10 mm, we will convert the given values of length of side in mm before putting the values in the formula

`For \: \: triangle ( a )</p><p>\qquad \sf{ h^2 = b^2 + p^2}`

`\qquad \sf{ h =√(b^2 + p^2)}`
`\qquad \sf{h=√( (12)^2 + (18)^2 )}`
`\qquad\sf{h=√( (12)^2 + (18)^2 )} \\ \\ \qquad \sf{ h= √(144 + 324)} \\ \\ \qquad \sf{ h = √(468)}</p><p> \\ \\\qquad\underline{\underline{\pmb{ \sf{ h = 21.63 mm}}}} \\ \\ For \: \: triangle ( b ) \qquad \sf{ h^2 = b^2 + p^2} \\ \\ \qquad \sf{h =√(b^2 + p^2) } \\ \\ \qquad \sf{ h = √((90)^2+(120)^2)} \\ \\ \qquad \sf{ h=√(8100+14400)} \\ \\ </p><p>\qquad \sf{ h =√(22500)} \\ \\\qquad\underline{\underline{\pmb{ \sf{h = 150mm}}} } \\ \\ For \: \: triangle ( c ) \qquad \sf{h^2 = b^2 + p^2 } \\ \\ \qquad \sf{ h=√(b^2 + p^2)} \\ \\\qquad\sf{ h=√((100)^2)+(50)^2)} \\ \\\qquad\sf{ h=√(10000+2500)} \\ \\ \qquad \sf{ h =√(12500)} \\ \\ </p><p>\qquad\underline{\underline{\pmb{\sf{h = 111.80mm}}} }`

Answer 2

Answers:

➝ Hypotenuse of triangle ( a ) = 21.63 mm

➝ Hypotenuse of triangle ( b ) = 150 mm

➝ Hypotenuse of triangle ( c ) = 111.80 mm

`\quad\rule{300pt}{1.5pt}\quad`

Solution:

We have to find the length of hypotenuse in the given 3 triangles, which can be done by using Pythagoras theorem.

• Pythagoras theorem states that :

" In a right angled triangle, the square of hypotenuse side is equal to the sum of square of other two sides "

`\qquad \bull \:{\pmb{\mathfrak{ h^2 = b^2 + p^2}}}`

And we have to convert the answer to the units indicated in red i.e, in mm.

Since 1cm = 10 mm, we will convert the given values of length of side in mm before putting the values in the formula

• For triangle ( a )

`:\implies\qquad \sf{ h^2 = b^2 + p^2}`

`:\implies\qquad \sf{ h =√(b^2 + p^2)}`

`:\implies\qquad \sf{h=√( (12)^2 + (18)^2 )}`

`:\implies\qquad \sf{ h= √(144 + 324)}`

`:\implies\qquad \sf{ h = √(468)}`

`:\implies\qquad\underline{\underline{\pmb{ \sf{ h = 21.63 mm}}}}`

• For triangle ( b )

`:\implies\qquad \sf{ h^2 = b^2 + p^2}`

`:\implies\qquad \sf{h =√(b^2 + p^2) }`

`:\implies\qquad \sf{ h = √((90)^2+(120)^2)}`

`:\implies\qquad \sf{ h=√(8100+14400)}`

`:\implies\qquad \sf{ h =√(22500)}`

`:\implies\qquad\underline{\underline{\pmb{ \sf{h = 150mm}}} }`

• For triangle ( c )

`:\implies\qquad \sf{h^2 = b^2 + p^2 }`

`:\implies\qquad \sf{ h=√(b^2 + p^2)}`

`:\implies\qquad \sf{ h =√((100)^2)+(50)^2)}`

`:\implies\qquad \sf{ h=√(10000+2500)}`

`:\implies\qquad \sf{ h =√(12500)}`

`:\implies\qquad \underline{\underline{\pmb{\sf{h = 111.80mm}}} }`