Question

The attitude of a right triangles is 7 cm less
than its base. If the hypotenuse is 13cm,
find the other two sides.​

Answer 1

Answer:

$\huge\red{ \bold{Given: }}$

• The attitude of a right triangles is 7 cm less
• The attitude of a right triangles is 7 cm lessthan its base. If the hypotenuse is 13cm

$\huge\red{ \bold{To \: Find: }}</p><p>$

• find the other two sides.

$\huge\red{ \bold{ Solution: }}</p><p>$

$\bold{Let \: x \: be \: the \: base \: of \: the \: triangle, \: then \: the \: altitude \: will be (x−7). }\\ </p><p></p><p> \bold{By \: Pythagoras \: theorem,} \\ \bold{ {x}^{2} + (x - {7})^{2} = ( {13}^{2} )} \\ \bold{ 2 {x}^{2} - 14x + 49 - 169 = 0} \\ \bold{ 2 {x}^{2} - 14x - 120 = 0} \\ \bold{{x}^{2} - 7x - 60 = 0} \\ \bold{ {x}^{2} - 12x + 5x - 60 = 0} \\ \bold{ (x - 12)(x + 5) = 0} \\ \bold{x = 12 \: x = - 5}$

Since the side of the triangle cannot be negative, so the base of the triangle is 12cm and the altitude of the triangle will be

$\pink{ \bold{12−7=5cm}}$

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