Question

The height of a triangle is 7cm less than its base if the hypotenuse is 13cm form the quadratic equation to find the base of the triangle.


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Answer 1

Given:-

The height of the triangle is 7cm less than its base.

The Hypotenuse = 13cm

To Find:-

The quadratic equation to find the base of the triangle

Solution:-

Let the base of the triangle be x

As, the height is 7cm less than the base.

Height of the triangle = (x - 7)

Hypotenuse = 13cm

By applying Pythagoras Theorem:-

$\sf Base^2 + Height^2 = Hypotenuse^2Base$

$\sf \implies x^2 + (x - 7)^2 = 13^2</p><p>$

$\sf \implies x^2 + (x)^2 -2(x)(7) + (7)^2 = 13^2$

$\sf \implies x^2 + x^2 - 14x + 49 = 169$

$\sf \implies 2x^2 - 14x + 49 - 169$

$\sf \implies 2x^2 - 14x - 120$

$\sf \implies 2(x^2 - 7x - 60)$

$\sf \implies x^2 - 7x - 60 = 0$

Answer 2

Answer:

Hope it will help

Explanation:

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