Question

Height of triangle =7cm less than its base
Hypotenuse =13cm
Find length of other two sides

Answer 1

Answer:

by Pythagoras theorem square root of hypotenuse is equal to sum of square of other two sides ,so 7^2-13^2=^120~ 3.12

Answer 2

Let base be x

According to problem,

Height is 7 cm less than base

So height = x -7

And also given, hypotenuse = 13 cm

By pythgerous Therom,

${h}^{2} = {s}^{2} + {s}^{2}$

Substitute all the values we get,

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

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

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

${2x}^{2} - 14x + 49 - 169 = 0$

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

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

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

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

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

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

$x + 5 = 0 \: \: or \: \: x - 12 = 0$

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

We know that, side never be negative

So, x = 12 cm

Base = 12 CM ; Height = 12-7 = 5CM

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