Question

A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 6 cm more than the shorter leg and the hypotenuse 12 cm more than the shorter leg. How long should the sides of the triangle​ be?

Answer 1

Answer:

18cm, 24cm, 30cm

Step-by-step explanation:

Let x be the length of the shorter leg

(x + 12)² = (x + 6)² + x²

x² + 24x + 144 = x² + 12x + 36 + x²

x² - 12x - 108 = 0

x² - 18x + 6x - 108 = 0

x(x - 18) + 6(x - 18) = 0

(x - 18)(x + 6) = 0

x = 18, -6

x = 18

x + 6 = 24

x + 12 = 30

Answer 2

Length of the sides of the triangles are 18 cm  , 24 cm , 30 cm

What is a triangle?

A figure bounded by 3 sides and all the internal angles add up to 180 ° is called a triangle.

What is a right angled triangle?

• A triangle in which one angle in 90°  is called a right angled triangle.
• The side opposite to the right angle is called the hypotenuse which is the longest side of the triangle.

How to know the lengths of the sides of the triangle?

Let the length of the shorter leg be x cm

According to the problem,

• The longer leg 6 cm more than the shorter leg

∴ Length of the longer leg = ( 6 + x) cm

Again,

• The hypotenuse 12 cm more than the shorter leg.

∴ Length of the hypotenuse = ( 12 + x) cm

Now, applying the Pythagorean theorem,

( 12 + x )² = x² + (x+ 6)²

⇒144 + x² + 24x = x² + x² + 36 + 12x

⇒ x² - 12x - 108 = 0

⇒x² - 18x + 6x - 108 = 0

⇒ x( x - 18) + 6( x - 18) = 0

⇒ (x - 18 )(x + 6) = 0

⇒ x = 18 or -6

Since x is a length of a side so the negative value is rejected

So, x= 18 cm

Length of the longer side = 24 cm

Length of the hypotenuse = 30cm

Find more about "Triangles" here : brainly.com/question/17335144

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