Question

The perimeter of a right triangle is 15 m, and the area is 10 m2. Then, the lengths of the sides are each multiplied by 3. What is the area of the new triangle? m2

Answer 1

Answer: 90m^2

Explanation: Cuz I just had this question an I'm to lazy to explain it. You're welcome for my help :)

Answer 2

The area is measurement of the surface of a shape.

The area of the new triangle is 270 square meters.

Let's denote the lengths of the sides of the right triangle as a, b, and c, where c is the hypotenuse. Then, we have:

a + b + c = 15 (perimeter of the triangle)

ab/2 = 10 (area of the triangle)

Since the triangle is right-angled, we can use the Pythagorean theorem to relate the sides:

$a^2 + b^2 = c^2$

Squaring the perimeter equation, we get:

$(a + b + c)^2 = 225\\a^2 + b^2 + c^2 + 2ab + 2bc + 2ca = 225$

Substituting $c^2 = a^2 + b^2$ and ab = 20 into this equation, we get:

$a^2 + b^2 + a^2 + b^2 + 2(20) + 2bc = 225\\2a^2 + 2b^2 + 2bc = 185\\a^2 + b^2 + bc = 92.5$

Multiplying the three sides of the triangle by 3, we get:

$3a + 3b + 3c = 45\\3ab/2 = 10*3^2/2 = 45$

The first equation gives us a + b + c = 15 after dividing both sides by 3. Dividing the second equation by$3^2/2$, we get:

$ab/2 = 45/(3^2/2) = 30$

So the sides of the new triangle are a'=3a, b'=3b, and c'=3c. The area of the new triangle is given by:

$a'b'/2 = (3a)(3b)/2 = 9(ab/2) = 9(30) = 270$

for such more question on perimeter

https://brainly.in/question/49134656

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