Question

Hey brainly users ☺☺☺
.
My Question is :-
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm find the other two sides

Answer 1

Let the altitude of the triangle be x.

The base hence is 7+x

We know by pythagoras theorem :

if h=hypotenuse,p=height,b=base.

h²=p²+b²

==> (13 cm)²=(x )²+(7cm + x)²

==> 169 cm² =x²  + 49 cm² + 14 cm x + x²

==> 2 x² + 14 cm x + 49 cm² - 169 cm² = 0

==> 2 x² + 14 cm x - 120 cm² = 0

==> 2 x² +24 cm x - 10 cm x -120 cm²=0

==> 2 x(x + 12 cm) - 10 cm ( x + 1 2 x  cm)

==> ( 2 x - 10 cm )( x + 12 cm ) = 0

Either 2 x= 10 cm ==> x= 5 cm

or , x = -12 cm but x cannot be negative so x= 5cm

The other 2 sides are x and 7 + x

==> 5 cm and 7+5 cm

==> 5 cm and 12 cm

The answer is 5 cm and 12 cm

Hope it helps you

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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