Question

The altitude of a right triangle is 7 cm less than its base the hypotenuse is 13 cm find the two sides

Answer 1

Answer:

Let the base =X

If the altitude is 7 less than the base

Therefore, (x-7) = altitude

Hypotenuse = 13

By Pythagoras theorem ---

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

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

2x^2-14x=169-49

2x^2-14x=120

2x^2-14x-120=0

X^2-7x-60=0

By factorize -----

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

X(x-12) +5(x-12) =0

X-12 =0

X=12

And

X+5=0

X=-5

Hence X= 12

Therefore , altitude = x-7= 12-7 =5

And base =X=12

______✔

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