Question

Modeling with mathematics - The Polygon - Perimeter Confusion!!In algebra class, the teacher, Ms. Hampton, read a brief history on “Who is Archimedes?”Ms. Hampton, then assigned a warm-up activity to connect students to prior knowledge. She asked them to determine the polygon and find its perimeter algebraically using the following information below.Given Information: The hypotenuse must have a length of t + 11.The lengths of the other two sides are t + 10 and t – 7.Susan was the first to respond. She claimed, based on her prior knowledge, that the polygon is a right triangle and you can use the formula P = 2l + 2w to find the perimeter of a right triangle. She showed her work below modeled by the triangular diagram she drew.P = 2l + 2wp = 2(t + 11) + 2(t + 10) + t – 7 p = 2t + 22 + 2t + 20 + t – 7p = 5t + 35 (units)Do you agree with 1) Susan’s diagram 2) perimeter formula and her 3) algebraic response? Create a written response that includes the following: Write a claim. Statements written in sentences that agrees or disagrees with the claim made in the scenario below. Provide evidence/justification and supported reasoning Write a counterclaim. Write a sentence that contradicts the claim made and clearly states your position. Explain the counterclaim you are making. The more “real” you make the opposing position, the more “right” you will seem when you disprove it using clear sentences and mathematical language. State a clear conclusion. A concluding statement that summarizes your claim

Answer 1

we have

c=t+11 -----> hypotenuse

a=t+10 ----> leg

b=t-7 -----> other leg

step 1

Apply the Pythagorean Theorem

c^2=a^2+b^2

(t+11)^2=(t+10)^2+(t-7)^2

t^2+22t+121=t^2+20t+100+t^2-14t+49

combine like terms

t^2+22t+121=2t^2+6t+149

the left side is not equal to the right side

that means

the given lengths, not satisfy the pythagorean Theorem

Is not a right triangle

The perimeter is equal to

P=(t+11)+(t+10)+(t-7)

P=(3t+14) units

therefore

I not agree with Susan's diagram

I not agree with perimeter formula

I not agree with algebraic response

A claim-----> if the triangle is a right triangle, then, must satisfy the Pythagorean Theorem