Question

Answer this question pls

Answer 1

Answer:

cb=41

Step-by-step explanation:

by pythagoras theorem

9 (square )+40 (square )=1681

under root of 1681 =41

ans =41

Answer 2

Given:

• CA = 9m
• AB = 40m

To Find:

• The measure of the side CB

Solution:

➤ Here, we have said that it's a right angled triangle and been provided with the measurements of 2 of its sides CA and AB respectively. Now, we're asked to find its third side CB by using suitable properties of triangles or appropriate theorems

${\rm{ \underline{ \underline{ \red{Pythagoras \: therom : }}}}}$

✦Pythagoras therom is a theorem which is only applicable for right - angled triangles where, it states that the sum of squares of both the sides is equal to the square of its hypotenuse.

${ \red{ \sf{Formula : }}}$

$\rm \: (Hypotenuse) {}^{2} = {(Base)}^{2} + {(Side)}^{2}$

${ \red{ \sf{Here : }}}$

↦ CA = Side

↦ AB = Base

↦ CB = Hypotenuse

${ \underline{ \underline{ \red{ \rm{Squaring \: sides \: we \: get : }}}}}$

$\rm \: {(CB)}^{2} = {(AB)}^{2} + {(CA)}^{2} \\ \\\rm \: {(CB)}^{2} = {( 9m)}^{2} + {(40m)}^{2} \\ \\ \rm {(CB)}^{2} = 81 {m}^{2} + 1600 {m}^{2} \\ \\ \rm {(CB)}^{2} = 1681 {m}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm {(CB)}^{2} = \sqrt{1681 {m}^{2} } \: \: \: \: \: \: \: \: \: \: \\ \\ \rm \: {(CB)}^{2} = {\red{ \underline{ \boxed{ \sf{41m}}} \star}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

${ \red{ \sf{Hence : }}}$

❂ The measure of the side CB is 41m

${ \underline{ \underline{ \rm{ \red{Verification : }}}}}$

We know that a triangle is formed only when the sum of two sides is more than the third side . Here (40 + 9) > 41 . This is means this combination is correct. Even if CB is Hypotenuse its the longest side which is proved as CB > 9,40

${ \underline{ \underline{ \rm{ \red{More \: to \: know : }}}}}$

✪ Heron's Therom ✪ 

◕Heron's formula, named after Hero of Alexandria, which gives the area of a triangle when the length of all three sides are known.

$\rm \: \sqrt{S (S - A) (S - B)( S - C)}$

★ Where,

• S Denotes Semiperimeter
• A,B,C are the Sides respectively

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