Studdy AI Logo
Math

QuestionCalcola perimetro e area di un triangolo rettangolo con cateti di 10 cm10 \mathrm{~cm} e 24 cm24 \mathrm{~cm}.

Studdy Solution

STEP 1

Assumptions1. We have a right triangle. . The lengths of the two legs (cateti) are given as10 cm and24 cm.
3. We need to find the perimeter and the area of the triangle.

STEP 2

First, we need to find the length of the hypotenuse (ipotenusa) using the Pythagorean theorem.
potenusa=Cateto12+Cateto22potenusa = \sqrt{Cateto1^2 + Cateto2^2}

STEP 3

Now, plug in the given values for the lengths of the two legs to calculate the length of the hypotenuse.
potenusa=102+242potenusa = \sqrt{10^2 +24^2}

STEP 4

Calculate the length of the hypotenuse.
potenusa=102+242=100+576=676=26 cmpotenusa = \sqrt{10^2 +24^2} = \sqrt{100 +576} = \sqrt{676} =26 \mathrm{~cm}

STEP 5

Now that we have the length of the hypotenuse, we can find the perimeter of the triangle. The perimeter is the sum of the lengths of all sides.
Perimetro=Cateto1+Cateto2+IpotenusaPerimetro = Cateto1 + Cateto2 + Ipotenusa

STEP 6

Plug in the values for the lengths of the two legs and the hypotenuse to calculate the perimeter.
Perimetro=10 cm+24 cm+26 cmPerimetro =10 \mathrm{~cm} +24 \mathrm{~cm} +26 \mathrm{~cm}

STEP 7

Calculate the perimeter of the triangle.
Perimetro=10 cm+24 cm+26 cm=60 cmPerimetro =10 \mathrm{~cm} +24 \mathrm{~cm} +26 \mathrm{~cm} =60 \mathrm{~cm}

STEP 8

Now that we have the perimeter, we can find the area of the triangle. The area of a right triangle is given by the formulaArea=12×Cateto1×Cateto2Area = \frac{1}{2} \times Cateto1 \times Cateto2

STEP 9

Plug in the values for the lengths of the two legs to calculate the area.
Area=2× cm×24 cmArea = \frac{}{2} \times \mathrm{~cm} \times24 \mathrm{~cm}

STEP 10

Calculate the area of the triangle.
Area=2×10 cm×24 cm=120 cm2Area = \frac{}{2} \times10 \mathrm{~cm} \times24 \mathrm{~cm} =120 \mathrm{~cm}^2The perimeter of the triangle is60 cm and the area is120 cm².

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord