Question

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

• A. 2,5
• B. 5,3
• C. 7,2
• D. 12,5

Answer 1

The correct option is D

12,5

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,

$bas{e}^2$+ $altitud{e}^2$ = $hypotenus{e}^2$

Substituting the values, we get

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

$\Rightarrow$ $x^2$ + $x^2$ + 49 – 14x = 169

$\Rightarrow$ 2$x^2$ – 14x + 49 – 169 = 0

$\Rightarrow$ 2$x^2$ – 14x – 120 = 0

Dividing with 2 on both sides the above equation simplifies to

$\Rightarrow$ $x^2$ – 7 x – 60 = 0

$\Rightarrow$ $x^2$ – 12 x + 5 x – 60 = 0

$\Rightarrow$ x ( x – 12) + 5 ( x – 12) = 0

$\Rightarrow$ ( x – 12)( x + 5) = 0

$\Rightarrow$ x – 12 = 0 or x + 5 = 0

$\Rightarrow$ x = 12 or x = –5

Length cannot be negative so x cannot be equal to – 5

base x = 12cm; altitude = 12 – 7 = 5cm