Question

The altitude of a right triangle is 7cm less than its base. If the hypotenuse is 13cm, find the other two sides. ​

Answer 1

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The altitude of a right triangle is 7cm less than its base. If the hypotenuse is 13cm, find the other two sides.

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⛥⛥ Refer the image ⛥⛥

$\tt{Let \: base \: of \: the \: right \: triangle \: = \: x \: cm}$

$\tt{Then \: it's \: altitude \: = \: x - 7 cm}$

$\underline\bold\purple{By\:Pythagoras\:Theorem}$

$\sf\red{(Base)^2\:+\:(Height)^2\:=\:(Hypotenuse)^2}$

⟹ x² + (x - 7)² = 13²

⟹ x² + x² - 14x + 49 = 169

⟹ 2x² - 14x + 49 - 169 = 0

⟹ 2x² - 14x - 120 = 0

⟹ x² - 7x - 60 = 0

⟹ x² - 12x + 5x - 60

⟹ x(x - 12) + 5(x - 12) = 0

⟹ (x - 12) (x + 5) = 0

⟹ x - 12 = 0 (or) x + 5 = 0

⟹ x = 12 (or) x = -5

$\tt{But\:x\:can't\:be\: negative}$

∴ x = 12

$\:\:$x - 7 = 12 - 7 = 5

∴ The two sides are = ${\red{\boxed{12\:cm}}}$ and ${\red{\boxed{5\:cm}}}$

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Answer 2

Step-by-step explanation:

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${\huge{\bold{\underline{\underline{Answer:}}}}}$

♡ ↪☛ Let the base = x cm

Given that The altitude of a right triangle is 7 cm less than its base

Altitude is = x - 7 cm

Given that hypotenuse = 13cm

Applying Pythagoras theorem,

base2+ altitude2 = hypotenuse2

plug the values we get

x2+ ( x – 7)2 = 132

x2+ x2+ 49 – 14 x = 169

2 x2 – 14 x + 48 – 169 = 0

2 x2 – 14 x – 120 = 0

Divide by 2 to both side to simplify it

x2 – 7 x – 60 = 0

x2 – 12 x + 5 x – 60 = 0

x ( x – 12) + 5 ( x – 12) = 0

( x – 12)( x + 5) = 0

x – 12 = 0 or x + 5 = 0

x = 12 or x = –5

length can not negative so that x can not equal to – 5

base x = 12cm

altitude = 12 – 7 = 5cm

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