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

Step-by-step explanation:

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Answer 2

Let x be the base of the right triangle

Perpendicular or altitude = x - 7cm

Hypotenuse = 13 cm

Using Pythagoras' Theorem,

${13}^{2} = {x}^{2} + {(x - 7)}^{2}$

$169 = {x}^{2} + {x}^{2} - 14x + 49$

$2 {x}^{2} - 14x - 120 = 0$

${x}^{2} - 7x - 60 = 0$

${x}^{2} - 12x + 5x - 60 = 0$

$x(x - 12) + 5(x - 12) = 0$

$(x - 12)(x + 5) = 0$

$x = 12 \: and \: x≠ - 5 \: since \: size \: cant \: be \\ negative \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$Base=x=12\:cm$

$Altitude=x-7\:cm=(12-7)\:cm=5\:cm$