Question

The altitude of right triangle is 7 cm less than its base. If the hypotenuse is 17 cm . Find the other two sides

Answer 1

Answer:

Let the base of the triangle be 'x'cm

then altitude=(x-7)cm

Hypotenuse=17cm

By Pythagoras theorem,

(x)²+(x-7)²=(17)²

x²+(x)²+(7)²-2(x)(7)=289

x²+x²+49-14x=289

2x²-14x+49-289=0

2x²-14x-240=0

2(x²-7x-120)=0

x²-7x-120=0/2

x²-7x-120=0

this equation cannot give real roots.

so hypotenuse should be 13cm.

then we will get

x²-7x-60=0

→x=12 and x=-5

base =12

Altitude (x-7)=12-7=5cm

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