Question

The hypotenuse of a right triangle is
25 cm. If one of the side is 7 cm, find the
length of the other side.explain with solution​

Answer 1

Given

• ABC is a right angled triangle.
• Hypotenuse (AC) = 25cm
• Perpendicular (AB) = 7cm

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To find

• Length of the base (BC).

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Solution

• Let the AC be the hypotenuse with 25 cm and AB be the perpendicular with 7 cm.
• Now we have to find BC (base).

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$\boxed{\rm{Since,\: it\: is\: a\: right\: angle\: triangle}}$

•°• According to the [ Pythagoras theorem ]

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

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$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{AC^2 = AB^2 + BC^2{\bigstar}}}}$

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$\large{\tt{\longmapsto{(25)^2 = (7)^2 + BC^2}}}$

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$\large{\tt{\longmapsto{625 = 49 + BC^2}}}$

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$\large{\tt{\longmapsto{BC^2 = 625 - 49}}}$

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$\large{\tt{\longmapsto{BC^2 = 576}}}$

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$\large{\tt{\longmapsto{BC = \sqrt{576}}}}$

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$\large{\bf{\longmapsto{BC = 24cm}}}$

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Hence,

• The length of another side, i.e., base is 24 cm.

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Answer 2

Question:-

The hypotenuse of a right triangle is 25 cm. If one of the side is 7 cm, find the length of the other side.

Answer:-

• The Perpendicular of triangle is 24 cm.

To find :-

• Third side of triangle

Solution:-

• Hypotenuse (h) = 25 cm
• Base (b) = 7 cm
• Perpendicular (p) = ?

According to Pythagoras theorem,

$\large{ \pink{ \underline{ \underline{ \purple{ \mathfrak{ {hypotenuse}^{2} = {base}^{2} + {perpendicular}^{2} }}}}}}$

According to question,

$\large{ \tt : \implies \: \: \: \: \: \: {25}^{2} = {7}^{2} + {p}^{2} }$

$\large{ \tt : \implies \: \: \: \: \: {p}^{2} = {25}^{2} - {7}^{2} }$

$\large{ \tt : \implies \: \: \: \: \: {p}^{2} = 625 - 49}$

$\large{ \tt : \implies \: \: \: \: \: {p}^{2} = 576}$

$\large{ \tt : \implies \: \: \: \: \: p = \sqrt{576} }$

$\large{ \tt : \implies \: \: \: \: \: p = 24 \: cm}$

• The Perpendicular of triangle is 24 cm.