Question

the altitude of a right angled triangle is 7cm less than its Base. if hypotenuse is 13cm first the other two sides. ​

Answer 1

$\huge{\bf{\orange{\fbox{\underline{\color{blue}{Answer}}}}}}$

Let the base be = x

=> altitiude = x- 7cm

$\huge{\bf{\red{\fbox{\underline{\color{green}{Pythagoras \:triplet}}}}}}$

H² = b² + p²

=> 13² = x² + x - 7²

=> 169 = x² + x - 49

$=> \: \sqrt{169} = x + x - 49$

=> 13 = 2x - 49

On transposing the terms:

=> 13 + 49 = 2x

=> 62 = 2x

$=> \: \frac{62}{2} = x$

$\huge{\bf{\yellow{\fbox{\underline{\color{X\:=31}}}}}}$

☆ Base = x = 31

¤ Altitude = x - 7 = 31 - 7

$\huge{\bf{\green{\fbox{\underline{\color{blue}{=\:24}}}}}}$

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