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 of the triangle.

Answer 1

Answer:

b=x,h:x-7, hyp.. =13

13^2 = x2 +(x-7)^2

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

o = 2x^2-14x -120

o = x^2-7x-60

= (x-12) (x+5)=o

X-12=o, x = 12=b

h=X-7,h=12-7=5

hypo..=13

5 cm12cm , are height and base resp:

.

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