Question

find the length of the hypotenuse in a right angled triangle
a) a=12cm ,b=9cm
b) a=8cm , b=15cm

explain​

Answer 1

CONCEPT :-

♦ Pythagoras Theorem :-

In a right angle triangle , sum of square of base and height is equal to square of hypotenuse.

★ Hypotenuse ² = Base² + Height²

SOLUTION :-

a) a = 12cm , b = 9cm

Here , we are given height and base of the right angled triangle. We have to find Hypotenuse.

→ Hypotenuse² = 12² + 9²

→ Hypotenuse² = 144 + 81

→ Hypotenuse² = 225

→ Hypotenuse = √225

→ Hypotenuse = 15cm

Hence , Hypotenuse is 15cm.

________________________

b) a = 8cm , b = 15cm

Similarly , base and height are given as 8cm and 15cm. We have to find Hypotenuse.

→ Hypotenuse² = 8² + 15²

→ Hypotenuse² = 64 + 225

→ Hypotenuse² = 289

→ Hypotenuse = √289

→ Hypotenuse = 17cm

Hence , Hypotenuse is 17cm.

Answer 2

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$\bold{Let \: the \: number \: be \: x}$

$\bf{According \: to \: the \: question}$

$\bold{\frac{2}{3}x \: = \frac{1}{3}x + 3 }$

$\bold{ \frac{2}{3} x - \frac{1}{3}x = 3 }$

$\bold{ \frac{2x - x}{3} = 3}$

$\bold \green{x = 9}$