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
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Answer 1

Answer:

Base = 12 cm , Altitude = 5 cm , hypotenuse = 13 cm

Step-by-step explanation:

let breadth = x cm

so length = x - 7 cm

hypotenuse = 13 cm

( As it is right angled triangle )

By pythagoras theorem ,

x^2 + ( x-7 )^2 = ( 13 )^2

x^2 + x^2 + 49 - 14x = 169

2x^2 - 14x - 120 = 0

x^2 - 7x - 60 = 0

x^2 - 12x + 5x - 60 = 0

x ( x - 12 ) + 5 ( x - 12 )

( x + 5 ) ( x - 12 )

x = -5 , 12

Sides of a triangle can never be negative

Therefore, x = 12

base = x = 12 cm

length = x - 7 = 12 - 7 = 5 cm

hope it helps.......

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Answer 2

Given,

• Altitude of right triangle is 7 cm less than its base.
• Hypotenuse is 13 cm.

To find,

• The other two sides.

Solution,

Let x be the base of the triangle

Then altitude will be (x-7)

We know that,

$\sf{Base^2+Altitude^2=Hypotenuse^2}$

So, by pythagoras theorem,

${x}^{2} + ( {x - 7)}^{2} = {13}^{2} \\ \\ ⟹2 {x}^{2} - 14x + 49 = 169 \\ \\ ⟹2 {x}^{2} - 14x + 49 - 169 = 0 \\ \\ ⟹2 {x}^{2} - 14x - 120 = 0 \\ \\ ⟹2( {x}^{2} - 7x - 60) = 0 \\ \\ ⟹ {x}^{2} - 7x - 60 = \frac{0}{2} \\ \\⟹ {x }^{2} - 7x - 60 = 0 \\ \\ ⟹ {x}^{2} - 12x + 5x - 60 = 0 \\ \\ ⟹x(x - 12) + 5(x - 12) = 0 \\ \\ ⟹(x - 12)(x + 5) = 0$

So, x = 12 or x = -5

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

And the altitude will be (12-7) = 5 cm