Question

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The altitude of a right angle triangle is 7cm less than it's base. If the hypotenuse is 13cm ,find the other two sides .
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Answer 1

Given:-

• Hypotenuse = 13cm

To Find:-

• the other two sides of right-angled triangle.

step-by-step solution:-

Let x be the base of the triangle, then the altitude will be (x−7).

By Pythagoras theorem,

• → x² +(x−7)² = (13)²
• → 2x² −14x + 49 − 169=0
• → 2x² −14x−120 = 0
• → x² − 7x − 60 = 0
• → x² − 12x + 5x − 60 = 0
• → (x − 12)(x + 5) = 0
• → x = 12,x = −5

Since the side of the triangle cannot be negative, so the base of the triangle is 12cm and,

the altitude of the triangle will be 12−7 = 5cm.

Answer 2

Step-by-step explanation:

base = x

altitude = x - 7

by Pythagoras theorem

Base² + height² = hypotenuse ²

${ x}^{2} + {(x - 7)}^{2} = {13}^{2} \\ {x}^{2} + {x }^{2} - 14x + 49 = 169 \\ 2 {x }^{2} - 14x + 49 - 169 = 0 \\ 2 {x}^{2} - 14x - 120= 0$

divide the above equation by 2 we get

${x}^{2} - 7x - 60 = 0 \\ {x }^{2} - 12x + 5x - 60 = 0 \\ x(x - 12) + 5(x - 12) \\ = (x - 12)(x + 5) = 0 \\ x = 12$

since x= -5 is neglected as it is negative.

$base \: equals \: 12 \\ height \: equals \: x - 7 = 12 - 7 \\ = 5$