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

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Answer 2

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:-

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

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

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

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

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

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

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

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