Test in geometry level 2

Geometry Level 2

In a right angled-triangle, if the length of the perpendicular is 5 cm and the sum of the base and the hypotenuse is 25 cm, find the lengths of base and hypotenuse.

Note:- Write the answer as $\frac {2bh+h}{25}$ , where

b=Base length

h=Hypotenuse length

Anybody can give the solution without using Pythagorean Triplets ?

The answer is 13.

2 solutions

Vishal S
Feb 8, 2015

Given

a=5 cm

b+c=25 cm---->(1)

By Pythagorean Theorem, $a^2$ + $b^2$ = $c^2$

$5^2$ + $b^2$ = $c^2$

$\Rightarrow$ 25= $c^2$ - $b^2$

$\Rightarrow$ 25=(c+b)(c-b)

$\Rightarrow$ 25=25(c-b)

$\Rightarrow$ c-b=1---->(2)

By solving (1) & (2), we get

c=13 cm, b=12 cm

By substituting the values of c and b in $\frac {2bh+h}{25}$ , we get

* $\frac {2(13)(12)+13}{25}$ *

= $\frac {312+13}{25}$

= $\frac {325}{25}$

=13

Therefore the answer is $\boxed{13}$

Gurbinder Sekhon
Mar 13, 2015

Common sense 13 plus twelve make 25 I just substituted that for the answer This doesn't require use of phythagorean triplets Mere effing common sense

Test in geometry level 2

The answer is 13.

2 solutions

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