Question

What must be the length of the remaining side of a triangle if the longest side is 17 cm and the other side is 8cm

Answer 1

ɢɪᴠᴇɴ:-

Length of longest side of a triangle ( hypotenuse) = 17 cm

Length of other side (base) = 8 cm

ᴛᴏ ғɪɴᴅ:-

Length of remaining side of the triangle.

sᴏʟᴜᴛɪᴏɴ:-

A right triangle or right-angled triangle is a triangle in which one angle is a right angle. The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the hypotenuse. The sides adjacent to the right angle are called legs.

As it is said the longest side therefore we can assume it as a right angled triangle.

Let the other side be s.

By Pythagoras Theorem,

$\large\Longrightarrow{\sf{{hypo}^{2}={base}^{2}+{s}^{2}}}$

$\large\Longrightarrow{\sf{{17}^{2}={8}^{2}+{s}^{2}}}$

$\large\Longrightarrow{\sf{289=64+{s}^{2}}}$

$\large\Longrightarrow{\sf{389-64={s}^{2}}}$

$\large\Longrightarrow{\sf{225={s}^{2}}}$

By square rooting both the sides,

$\large\Longrightarrow{\sf{\sqrt{225}=s}}$

$\large\Longrightarrow{\sf{15=s}}$

$\large\blue\therefore\boxed{\sf{\blue{s=\:\frac{+}{-}\:15}}}$

ɴᴏᴡ ʟᴇᴛ's ᴠᴇʀɪғʏ ɪᴛ:-

By Pythagoras Theorem,

$\large\Longrightarrow{\sf{{hypo}^{2}={base}^{2}+{s}^{2}}}$

By putting the values,

$\large\Longrightarrow{\sf{{17}^{2}={8}^{2}+{15}^{2}}}$

$\large\Longrightarrow{\sf{289=64+225}}$

$\large\Longrightarrow{\sf{289=289}}$

$\large\therefore\boxed{\sf{LHS=RHS}}$

$\huge\green\therefore\boxed{\sf{\green{The\: remaining \:side \:of \:the\: triangle \:is \:\frac{+}{-}\:15}}}$

Answer 2

Given :- The longest side of the triangle is 17 cm and other side is 8 cm .

To Find :- Length of Third side of triangle ?

Concept used :-

• Sum of any two sides of a ∆ is greater than the third side .
• Difference between any two sides of a ∆ is smaller than the third side .

Solution :-

Let us assume that, third side of the triangle is equal to x cm .

So,

→ Sum of first two sides = 17 + 8 = 25

→ Difference between first two sides = 17 - 8 = 9

then,

→ Difference between first two sides < Third side < Sum of first two sides .

→ 9 < x < 25 .

therefore,

→ Length of third of the given triangle can be = 10, 11, 11.5 , 15.6, 20, 24 etc .

also, if we take only integer values then,

→ Length of third of the given triangle can be = 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 or 24 .

Extra knowledge :-

If we assume the given triangle is a right angled ∆ with longest side as 17 cm and other side as 8 cm .

So,

→ Hypotenuse = Length of longest side = 17 cm .

→ Other side = 8 cm

→ Third side = Let x cm .

then,

→ x = √{(Hypotenuse)² - (Other side)²} { By pythagoras theorem }

→ x = √(17² - 8²)

→ x = √(289 - 64)

→ x = √(225)

→ x = 15 cm (Ans.)

therefore, for a right angled triangle length of the third side is equal to 15 cm .

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