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Q. two sides been given calculate the side marked by a letter in each right angled triangle​

Answer 1

Question :-

Two sides been given calculate the side marked by a letter in each right angled triangle

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Solution :-

➲ Given Information :-

• Altitude of the Triangle ➢ 21 units
• Hypotenuse of the Triangle ➢ 29 units
• 29 unitsRight Angled Triangle

➲ To Find :-

• Base of the Triangle ( d )

➲ Concept :-

• Pythagoras Theorem and it's uses

➲ Formula Used :-

• Pythagoras Theorem $\boxed{ \boxed{ \bf{ \red{Hypotenuse^ {2} } = \blue{ Altitude^{2} }+ \green{Base ^{2} }}}}$

➲ Explanation :-

• We will simply substitute the given values in the formula mentioned above, Since we need to find the base ( d ) of the triangle, We will make it he subject of formula and will bring all the other values to the Right Hand Side of the equation. Then after some minute calculations, We will have the value of the base of our right angled triangle.

➲ Calculation :-

Using Pythagoras Theorem,

$\rm{: \implies\boxed{ \boxed{ \rm { \red{Hypotenuse^ {2} } = \blue{ Altitude^{2} }+ \green{Base ^{2} }}}}}$

Substituting the values given in the formula, We get,

$\rm{: \implies\rm{ \red{(29)^ {2} } = \blue{ (21)^{2} }+ \green{Base ^{2} }}}$

Transposing (21)² to Left Hand Side and keeping Base² to the Right Hand Side of the equation

$\rm : \implies\rm{ - \blue{ ( 21)^{2} } + \red{(29)^{2} } = \green{ (base) ^{2} }}$

Simplifying further, We get,

$\rm : \implies\rm{ \blue{ - 441} + \red{841 } = \green{(base)^{2} }}$

Adding up 441 & 841, We get,

$\rm : \implies\rm{ \purple{400} = \green{(base)^{2} }}$

Now, finding the base, We will send the exponent ( ² ) to Left Hand Side of the equation, Making it an under root of 400, We get,

$\rm: \implies \purple{\sqrt{400}} = \green {base}$

We know, 400 is the square of 20. Therefore,

$\bf: \implies \purple{20 \: units} = \green{base}$

∴ Base of the right angled triangle is 20 units.

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Final Answer :-

• The base of Right Angled Triangle ( d ) = 20 units

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Note :-

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