Question

2 points
3. In a right-angled triangle,
find the length of the
hypotenuse if the height is 15
cm and the base is 8 cm.​

Answer 1

✬ Hypotenuse = 17 cm ✬

Explanation:

Given:

• Triangle is right angled.
• Height of triangle is 15 cm.
• Length of base of triangle is 8 cm.

To Find:

• Length of hypotenuse of triangle ?

Solution: Let in a right angled ∆ABC , right angled at B. We have

• AB {perpendicular/height} = 15 cm

• BC {base} = 8 cm

• AC {hypotenuse} = ?

We can find length of AC by using Pythagoras theorem.

★ H² = Perpendicular² + Base² ★

➨ AC² = AB² + BC²

➨ AC² = 15² + 8²

➨ AC² = 15 × 15 + 8 × 8

➨ AC² = 225 + 64

➨ AC = √289 = √17 × 17

➨ AC = 17 cm

Hence, we got the length of AC i.e Hypotenuse of ∆ABC as 17 cm.

______________

[ Let's Check ]

• AC² = AB² + BC²
• 17² = 15² + 8²
• 289 = 225 + 64 = 289

$\large\bold{\texttt {Verified }}$

1. Pythagoras Theorem - “In a right-angled triangle, the square of the hypotenuse (long) side is equal to the sum of squares of the other two sides“.

Answer 2

$\Large{\underline{\bf{\color{cyan}GiVeN,}}}$

$\bf\blue{In\:a\:right\:angle\:\triangle,}$

• Height is 15 cm.

• Base is 8 cm.

$\Large{\underline{\bf{\color{coral}To\:FiNd,}}}$

• The length of the hypotenuse.

$\Large{\underline{\bf{\color{lime}CaLcUlAtIoN,}}}$

$\bf\purple{As\:we\:know\:that,}$

➙ In order to calculate the length of the hypotenuse of a right angle triangle, we can use the Pythagorean Theorem.

➙ It states that the total of the squares of the lengths of the two shorter sides (Height & Base) of the right angle triangle is equivalent to the square of the length of the hypotenuse.

$\bf\pink{According\:to\:Pythagorean\:theorem,}$

$\red\bigstar\:\:{\underline{\green{\boxed{\bf{\color{peru}(Hypotenuse)^2\:=\:(Height)^2\:+\:(Base)^2\:}}}}}$

$:\implies\:\:\bf{(Hypotenuse)^2\:=\:(15)^2\:+\:8^2\:}$

$:\implies\:\:\bf{(Hypotenuse)^2\:=\:225\:+\:64\:}$

$:\implies\:\:\bf{(Hypotenuse)^2\:=\:289\:}$

$:\implies\:\:\bf{Hypotenuse\:=\:\sqrt{289}\:}$

$:\implies\:\:\bf\green{Hypotenuse\:=\:17\:cm}$

━─━─━─━─━─━─━─━─━─━─━─━─━─━─━

$\Large\bold\orange{Therefore,}$

The length of the hypotenuse is 17 cm.