# {\$${\red{\underline{\overline{ǫᴜᴇsᴛɪᴏɴ:-}}}}$$The altitude of a right angle triangle is 7cm

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$${\red{\underline{\overline{ǫᴜᴇsᴛɪᴏɴ:-}}}}$$

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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### 2 thoughts on “{<br />\<br />$${\red{\underline{\overline{ǫᴜᴇsᴛɪᴏɴ:-}}}}$$<br /><br /><br />The altitude of a right angle triangle is 7cm”

1. 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.

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

2. ### Given:–

• Hypotenuse = 13cm

### ToFind:–

• the other two sides of right-angled triangle.

### step-by-stepsolution:–

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.