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​

Answer 1

Answer:

Let the base be x and altitude be x - 7 ,

AC = 13 cm

According to Pythagoras theorem

AC² = AB² + BC²

13² = x² + (x - 7)²

169 = x² + x² - 2(7)x + 7²

169 = 2x² - 14 x + 49

169 - 49 = 2x² - 14 x

2x²- 14 x - 120 = 0 divide by 2

x² - 7x - 60 = 0

x² - 12x + 5x - 60 = 0

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

x + 5 = 0 x - 12 = 0

x = -5 x = 12

Side cannot be negative so

base= x = 12 cm

Altitude = 12 - 7 = 5cm

Thank you

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